Chapter 2, Problem 1PP

(General math) a. Design, write, compile, and run a C++ program that calculates and displays the area of a triangle, such as the one in Figure 2.18, with a base of 1 in and a height of 1.5 in. The area is given by this formula:

$\text{Area = 1×2 }\left(\text{base}\right)\text{ × }\left(\text{height}\right)$

b. Manually check the values computed by your program. After verifying that your program is working correctly, modify it to determine the area of a two-dimensional triangle with a base of 3.5 in and a height of 1.45 in.

Program Plan Intro

Program plan:

In the coding window, write the necessary code:

• To Declarethree float variable base=1, height=1.5 and area.
• To calculate the area of triangle.
• To display the calculated area of triangleto user.

Program description:

The main purpose of the program is to calculate the area of triangle with the given height and radius.In the main method,calculating the area of triangle with the given base and height and finally, displaying the output of area of triangle to user.

Explanation of Solution

Given information:

  $Area=\frac{1}{2}\times base\times height$

  $base=1in$

  $height=1.5in$

Program:

Program code to calculate the area of triangle:

//importing essential header files
#include<iostream>
//using namespace standards
usingnamespace std;
//main method
int main()
{
//declaring variables
float base=1;
float height=1.5;
float area;
//calculating area
    area=height*base/2;
//displaying area to user
    cout<<"area of triangle with base "<<base<<" inch and height "<<height <<" inch  is "<<area<<"sq. inch";
return0;
}

Explanation:

In the main method, three float variable base=1, height=1.5 and area are declared. After that the area of triangle is calculated by using the below given formula:

  $Area=\frac{1}{2}\times base\times height$

And the finally, calculated results are displayed to user.

Output:

Output of the above given program code:

  

Program Plan Intro

To verify the results produced by above program and then use the above program to calculate area of two-dimensional triangle whose base in 3.5in and height 1.5 in.

Explanation of Solution

Given information:

  $Area=\frac{1}{2}\times base\times height$

  $base=1in$

  $height=1.5in$

Explanation:

Firstly, verifying the results calculate by the above program.

  $Area=\frac{1}{2}\times base\times height$

  $base=1in$

  $height=1.5in$

Putting the given values in the above formula,

  $Area=\frac{1}{2}\times 1in\times 1.5in=0.75i{n}^2$

Thus, the calculated results are correct.

Now, modifying the program code to calculate the area of triangle with the given height =1.45 inch and base =3.5 inch.

Program code:

//importing essential header files
#include<iostream>
//using namespace standards
usingnamespace std;
//main method
int main()
{
//declaring variables
float base=3.5;
float height=1.45;
float area;
//calculating area
    area=height*base/2;
//displaying area to user
    cout<<"area of triangle with base "<<base<<" inch and height "<<height <<" inch  is "<<area<<"sq. inch";
return0;
}

Explanation:

In this program, in the main method, three float variable base=3.5, height=1.45 and area are declared. After that the area of triangle is calculated by using the below given formula:

  $Area=\frac{1}{2}\times base\times height$

And the finally, calculated results are displayed to user.

Output: