Calculating the Area of a Triangle Using Heron’s Formula in C++

Problem Description

We are given the three sides of a triangle, and we have to calculate the area of the triangle using Heron's formula. In this article, we are going to discuss how we can calculate the area of a triangle using Heron's Formula in C++.

Heron's Formula

The formula for calculating the semi-perimeter of the triangle is:

s = (a + b + c) / 2

Then, apply Heron's formula to calculate the area of the triangle.

Heron's formula for calculating the area of the triangle is:

Area = ? s * (s - a) * (s - b) * (s - c)

Return the area of the triangle after calculating.

Examples

Here are the examples with input and output values:

Example 1

• Input
  a = 5
  b = 12
  c = 13
• Output
  30

Explanation

The three sides of the triangle are: a = 5, b = 12, and c = 13.

The Semi-perimeter of the triangle: s = (a + b + c) / 2 = (5 + 12 + 13) / 2 = 15.

The area of the triangle: Area = ?15 * (15 - 5) * (15 - 12) * (15 - 13)
?15 * 10 * 3 * 2 = ?900 = 30.

Example 2

• Input
  a = 7
  b = 24
  c = 25
• Output
  84

Explanation

The three sides of the triangle are: a = 7, b = 24, and c = 25.

The Semi-perimeter of the triangle: s = (a + b + c) / 2 = (7 + 24 + 25) / 2 = 28.

The area of the triangle: Area = ?28 * (28 - 7) * (28 - 24) * (28 - 25)
?28 * 21 * 4 * 3 = ?7056 = 84.

Example 3

• Input
  a = 6
  b = 8
  c = 10
  
• Output
  24

Explanation

The three sides of the triangle are: a = 6, b = 8, and c = 10.

The Semi-perimeter of the triangle: s = (a + b + c) / 2 = (6 + 8 + 10) / 2 = 12.

The area of the triangle: Area = ?12 * (12 - 6) * (12 - 8) * (12 - 10)
?12 * 6 * 4 * 2 = ?576 = 24.

Calculating Area of a Triangle Using Heron's Formula

To calculate the area of a triangle, we use the direct formula to calculate the area of a triangle. We use Heron's formula to calculate the area of the triangle. We first calculate the semi-perimeter of the triangle.

Implementation Code

#include<bits/stdc++.h>
using namespace std;

double areaOfTriangle(double a, double b, double c) {
    // Step 1: Calculate the semi-perimeter
    double s = (a + b + c) / 2;
    
    // Step 2: Apply Heron's Formula
    double area = sqrt(s * (s - a) * (s - b) * (s - c));
    
    return area;
}

int main() {
    double a = 5;
    double b = 12;
    double c = 13;

    // Calculate the area
    double area = areaOfTriangle(a, b, c);
    
    // Output the result
    cout << "The area of the triangle is: " << area << endl;
    
    return 0;
}

Output

The area of the triangle is: 30

Time Complexity: O(1)
Space Complexity: O(1)