Chapter 6, Problem 19E

Question

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Answer 1

Question

Chapter 6, Problem 19E

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

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Answer 2

Question

Chapter 6, Problem 19E

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

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Answer 3

Question

Chapter 6, Problem 19E

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 6, Problem 19E

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

Answer 6

Expert Solution & Answer

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.

Answer 7

Expert Solution & Answer

Answer 8

Expert Solution & Answer

Answer 9

To determine

To write:

A script that will prompt the user to enter the coordinates of three points that determine a triangle, then calculate and print the area of the triangle and then call one function to formulate the area of the triangle by calling a local function that calculates the side lengths formed by any two points.

Answer 10

Answer to Problem 19E

Solution:

The script file is,

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

The function file is,

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Answer 11

Explanation of Solution

The given two points are (x1,y1) and (x2,y2).

The formula of the distance between the two points is given as,

distance=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

distance=(0−5)2+(0−0)2distance=5

Consider the three points are (0,0), (5,0) and (5,5).

The side of the triangle is,

a=(x1−x2)2+(y1−y2)2

Substitute 0 for x1, 5 for x2, 0 for y1 and 0 for y2 in the above formula.

a=(0−5)2+(0−0)2=5

The side of the triangle is,

b=(x2−x3)2+(y2−y3)2

Substitute 5 for x2, 5 for x3, 0 for y2 and 5 for y3 in the above formula.

b=(5−5)2+(0−5)2=5

The side of the triangle is,

c=(x3−x1)2+(y3−y1)2

Substitute 5 for x3, 0 for x1, 5 for y3 and 0 for y1 in the above formula.

c=(5−0)2+(5−0)2=52

The formula for half sum of the sides of the triangle is,

s=a+b+c2

Substitute 5 for a, 5 for b and 52 for c in the above formula.

s=5+5+522=8.5355

The formula for the area of the triangle is,

area=s(s−a)(s−b)(s−c)

Substitute 5 for a, 5 for b, 52 for c and 8.5355 for s in the above formula.

area=8.5355(8.5355−5)(8.5355−5)(8.5355−52)=12.5000

MATLAB Code:

% MATLAB code to calculate the area of the triangle by calling a function.

%script file.

x1 = input('the x coordinate of the fist point is entered:');

%enter the x coordinate of the first point.

x2 = input('the x coordinate of the second point is entered:');

%enter the x coordinate of the second point.

x3 = input('the x coordinate of the third point is entered:');

%enter the x coordinate of the third point.

y1 = input('the y coordinate of the fist point is entered:');

%enter the y coordinate of the first point.

y2 = input('the y coordinate of the second point is entered:');

%enter the y coordinate of the second point.

y3 = input('the y coordinate of the third point is entered:');

%enter the y coordinate of the third point.

Area = trianglearea(x1, y1, x2, y2, x3, y3);

fprintf('The triangle’’s area is %.2f\n', Area)

% end of script file

%The script file should be placed in the same folder.

% MATLAB code to calculate the area of the triangle.

%function file.

function out = trianglearea(x1, y1, x2, y2, x3, y3)

%define the area of triangle by using the function areatriangle.

a = sidetriangle(x1, y1, x2, y2);

%define the variable a.

b = sidetriangle(x2, y2, x3, y3);

%define the variable b.

c = sidetriangle(x3, y3, x1, y1);

%define the variable c.

s = (a+b+c)/2;

%define the variable s.

out = sqrt (s*(s-a)*(s-b)*(s-c));

end

function out2 = sidetriangle(x1, y1, x2, y2)

%calculate the distnace between the two points by calling a function

%sidetriangle.

out2 = sqrt((x1-x2)^2 + (y1-y2)^2);

%calculate the sides of the triangle.

end

% end of function

%The function file should be placed in the same folder.

Save the MATLAB script with name, mainscript.m, and the function file is trianglearea.m in the current folder. Execute the program by typing the script name at the command window to generate result.

Result:

The output is,

Matlab, Fourth Edition: A Practical Introduction to Programming and Problem Solving, Chapter 6, Problem 19E

Therefore, the result is stated above.