Chapter 6, Problem 21E

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 calculate the area of the triangle by calling a local function that calculates the length of the side formed by any two points.

Answer to Problem 21E

Solution:

The function file is,

% MATLAB code to calculate the side length of the triangle.

%function file.

function [out] = sidetriangle(x1, y1, x2, y2)

%define the side of the triangle by using the function sidetriangle.

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

end

% end of function

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

The function file to calculate the area is,

% MATLAB code to calculate the area of the triangle and print the result.

%function file.

function areatriangle(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.

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

fprintf('Area of the triangle is %3.2f\n', area);

%print the area of the triangle.

end

% end of function

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

The script file is,

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

%script file.

point1 = input('the coordinates of the fist point is entered:');

%enter the coordinates of the first point.

point2 = input('the coordinates of the second point is entered:');

%enter the coordinates of the second point.

point3 = input('the coordinates of the third point is entered:');

%enter the coordinates of the third point.

x1 = point1(1);y1 = point1(2);

%define the variable x1.

x2 = point2(1);y2 = point2(2);

%define the variable x2.

x3 = point3(1);y3 = point3(2);

%define the variable x3.

areatriangle(x1, y1, x2, y2, x3, y3)

% end of file

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

Explanation of Solution

The given two points are $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$.

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

$\text{distance}=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}$

Substitute 0 for $x_1$, 5 for $x_2$, 0 for $y_1$ and 0 for $y_2$ in the above formula.

$\begin{array}{l}\text{distance}=\sqrt{{\left(0-5\right)}^2+{\left(0-0\right)}^2}\\ \text{distance}=5\end{array}$

Consider the three points are $\left(0,0\right)$, $\left(5,0\right)$ and $\left(5,5\right)$.

The side of the triangle is,

$\text{a}=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}$

Substitute 0 for $x_1$, 5 for $x_2$, 0 for $y_1$ and 0 for $y_2$ in the above formula.

$\begin{array}{l}\text{a}=\sqrt{{\left(0-5\right)}^2+{\left(0-0\right)}^2}\\ \text{a}=5\end{array}$

The side of the triangle is,

$\text{b}=\sqrt{{\left(x_2-x_3\right)}^2+{\left(y_2-y_3\right)}^2}$

Substitute 5 for $x_2$, 5 for $x_3$, 0 for $y_2$ and 5 for $y_3$ in the above formula.

$\begin{array}{l}\text{b}=\sqrt{{\left(5-5\right)}^2+{\left(0-5\right)}^2}\\ \text{b}=5\end{array}$

The side of the triangle is,

$\text{c}=\sqrt{{\left(x_3-x_1\right)}^2+{\left(y_3-y_1\right)}^2}$

Substitute 5 for $x_3$, 0 for $x_1$, 5 for $y_3$ and 0 for $y_1$ in the above formula.

$\begin{array}{l}\text{c}=\sqrt{{\left(5-0\right)}^2+{\left(5-0\right)}^2}\\ \text{c}=5\sqrt{2}\end{array}$

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

$\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}$

Substitute 5 for a, 5 for b and $5\sqrt{2}$ for c in the above formula.

$\begin{array}{l}\text{s}=\frac{5+5+5\sqrt{2}}{2}\\ \text{s}=8.5355\end{array}$

The formula for the area of the triangle is,

$\text{area}=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

Substitute 5 for a, 5 for b, $5\sqrt{2}$ for c and $8.5355$ for s in the above formula.

$\begin{array}{l}\text{area}=\sqrt{8.5355\left(8.5355-5\right)\left(8.5355-5\right)\left(8.5355-5\sqrt{2}\right)}\\ \text{area}=12.5000\end{array}$

MATLAB Code:

clc

clear all

close all

% MATLAB code to calculate the side length of the triangle.

%function file.

function [out] = sidetriangle(x1, y1, x2, y2)

%define the side of the triangle by using the function sidetriangle.

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

end

% end of function

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

% MATLAB code to calculate the area of the triangle and print the result.

%function file.

function areatriangle(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.

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

fprintf('Area of the triangle is %3.2f\n', area);

%print the area of the triangle.

end

% end of function

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

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

%script file.

point1 = input('the coordinates of the fist point is entered:');

%enter the coordinates of the first point.

point2 = input('the coordinates of the second point is entered:');

%enter the coordinates of the second point.

point3 = input('the coordinates of the third point is entered:');

%enter the coordinates of the third point.

x1 = point1(1);y1 = point1(2);

%define the variable x1.

x2 = point2(1);y2 = point2(2);

%define the variable x2.

x3 = point3(1);y3 = point3(2);

%define the variable x3.

areatriangle(x1, y1, x2, y2, x3, y3)

% end of file

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

Save the MATLAB scripts with names, sidetriangle.m, areatriangle.m and areacall.m in the current folder. Execute the script by typing the script name at the command window to generate result.

Result:

The results are,

Therefore, the results and script files are stated above.