C Program To Determine The Area Of Any Triangle By Herons Formula

Calculating the area of a triangle when only its three side lengths are known can be achieved efficiently using Heron's Formula. In this article, you will learn how to implement Heron's formula in a C program to determine the area of any given triangle.

Problem Statement

Determining the area of a triangle typically requires its base and corresponding height. However, in many practical scenarios, these measurements are not readily available; instead, only the lengths of the three sides are known. The challenge is to compute the area accurately using only these three side lengths.

Example

Consider a triangle with side lengths 3, 4, and 5 units. The program should calculate and output its area.

Area of the triangle: 6.00 square units

Background & Knowledge Prerequisites

To understand and implement the C program for Heron's Formula, readers should have a basic grasp of:

• C Programming Fundamentals: Variables, data types (especially float or double), input/output operations (printf, scanf).
• Arithmetic Operators: Addition, subtraction, multiplication, division.
• Mathematical Functions: Understanding how to use functions from the library, specifically sqrt() for square root calculations.
• Conditional Statements: Basic if statements for input validation (e.g., checking for valid triangle sides).

Relevant Imports and Setup:

The program will require the header for standard input/output operations and for the sqrt() function. When compiling, you might need to link the math library using the -lm flag (e.g., gcc your_program.c -o your_program -lm).

Use Cases or Case Studies

Heron's Formula is invaluable in various fields where direct height measurement is impractical or impossible:

• Land Surveying: Surveyors often measure boundary lengths of triangular plots. Heron's Formula allows them to calculate the area without needing to establish perpendicular heights, especially on uneven terrain.
• Architecture and Construction: Calculating material requirements for triangular facades, roofs, or structural elements where only edge lengths are defined.
• Computer Graphics: In game development or rendering engines, triangle meshes form the basis of 3D objects. Calculating the area of these triangles can be useful for various algorithms like texture mapping or collision detection.
• Physics and Engineering: Determining the surface area of irregular components or stress distribution over triangular cross-sections where only linear dimensions are known.
• Mathematics Education: As a fundamental concept taught in geometry, illustrating how areas can be derived from perimeter information.

Solution Approaches

Heron's Formula provides a robust method for calculating the area of a triangle given its three side lengths.

Heron's Formula Implementation

This approach directly applies Heron's Formula to compute the area.

One-line summary: Calculate the semi-perimeter and then use it in Heron's formula to find the area of a triangle.

Code Example:

// Triangle Area using Heron's Formula
#include <stdio.h>
#include <math.h> // Required for sqrt() function

int main() {
    double side1, side2, side3; // Declare variables for side lengths
    double semiPerimeter;       // Variable for semi-perimeter
    double area;                // Variable to store the calculated area

    // Step 1: Prompt user for input
    printf("Enter the length of side 1: ");
    scanf("%lf", &side1);

    printf("Enter the length of side 2: ");
    scanf("%lf", &side2);

    printf("Enter the length of side 3: ");
    scanf("%lf", &side3);

    // Step 2: Validate if the input sides can form a triangle
    // The sum of any two sides must be greater than the third side
    if (side1 + side2 > side3 && side1 + side3 > side2 && side2 + side3 > side1) {
        // Step 3: Calculate the semi-perimeter (s)
        semiPerimeter = (side1 + side2 + side3) / 2;

        // Step 4: Apply Heron's Formula
        // Area = sqrt(s * (s - a) * (s - b) * (s - c))
        area = sqrt(semiPerimeter * (semiPerimeter - side1) *
                    (semiPerimeter - side2) * (semiPerimeter - side3));

        // Step 5: Display the calculated area
        printf("The area of the triangle is: %.2lf square units\\n", area);
    } else {
        // Step 6: Handle invalid triangle input
        printf("Error: The given side lengths cannot form a valid triangle.\\n");
        printf("Please ensure that the sum of any two sides is greater than the third side.\\n");
    }

    return 0;
}

Run

Sample Output:

Enter the length of side 1: 3
Enter the length of side 2: 4
Enter the length of side 3: 5
The area of the triangle is: 6.00 square units

Another example:

Enter the length of side 1: 7
Enter the length of side 2: 10
Enter the length of side 3: 5
The area of the triangle is: 16.25 square units

Example with invalid input:

Enter the length of side 1: 1
Enter the length of side 2: 2
Enter the length of side 3: 5
Error: The given side lengths cannot form a valid triangle.
Please ensure that the sum of any two sides is greater than the third side.

Stepwise Explanation:

1. Include Headers: The program starts by including for input/output functions (printf, scanf) and for the sqrt() function.
2. Declare Variables: double data type is used for side1, side2, side3, semiPerimeter, and area to handle decimal values and ensure precision in calculations.
3. Get Input: The program prompts the user to enter the lengths of the three sides using printf and stores them in the respective double variables using scanf("%lf", ...).
4. Validate Triangle: An if statement checks the triangle inequality theorem: the sum of any two sides must be greater than the third side. If this condition is not met, an error message is displayed, and the program exits without calculation.
5. Calculate Semi-Perimeter: If the sides are valid, the semi-perimeter (s) is calculated as half the sum of the three sides: s = (side1 + side2 + side3) / 2;.
6. Apply Heron's Formula: The area is then computed using the formula area = sqrt(s * (s - side1) * (s - side2) * (s - side3));. The sqrt() function from is crucial here.
7. Display Result: Finally, the calculated area is printed to the console, formatted to two decimal places using %.2lf.

Conclusion

Heron's Formula provides an elegant and practical method for calculating the area of any triangle when only its three side lengths are known. This C implementation demonstrates its straightforward application, including essential input validation to ensure meaningful results.

Summary

• Heron's Formula allows calculating a triangle's area using only its three side lengths.
• The formula requires first computing the semi-perimeter s = (a + b + c) / 2.
• The area is then A = sqrt(s * (s - a) * (s - b) * (s - c)).
• The C implementation involves reading three side lengths, validating them to ensure they form a valid triangle, calculating the semi-perimeter, and then applying the formula using sqrt() from .
• Remember to link the math library with -lm during compilation (e.g., gcc program.c -o program -lm).