C Program To Determine Which Triangle Is Greater In Term Of Area

Comparing the areas of different triangles is a common task in geometry and various practical applications. Understanding how to calculate and compare these areas programmatically allows for efficient analysis and decision-making.

In this article, you will learn how to write a C program to compare the areas of two triangles, determining which one is greater or if they are equal.

Problem Statement

The core problem involves receiving dimensions for two distinct triangles, calculating the area of each, and then comparing these calculated areas to identify which triangle possesses a larger area or if their areas are identical. This is crucial in scenarios like land division, optimizing material usage in design, or even in computer graphics for simple geometric comparisons.

Example

Consider two triangles: - Triangle 1 with base = 6 units, height = 4 units. - Triangle 2 with base = 5 units, height = 6 units.

The program should output something similar to this:

Triangle 1 Area: 12.00
Triangle 2 Area: 15.00
Triangle 2 is greater than Triangle 1.

Background & Knowledge Prerequisites

To follow this article, you should have a basic understanding of:

• C Programming Basics: Variables, data types (especially float or double for precision), input/output operations (scanf, printf).
• Conditional Statements: if-else constructs for making comparisons.
• Basic Geometry: The formula for the area of a triangle (Area = 0.5 * base * height) and Heron's formula (for area given three sides).
• Mathematical Functions: Using sqrt() from math.h for Heron's formula.

You will need to include the stdio.h header for standard input/output and math.h if using Heron's formula.

Use Cases or Case Studies

Comparing triangle areas can be applied in various real-world scenarios:

• Land Surveying and Real Estate: Determining which of two triangular plots of land is larger for valuation or division purposes.
• Architectural Design: Optimizing the use of triangular elements in construction, comparing the surface areas of different roof sections or structural components.
• Computer Graphics and Game Development: In 2D game engines, comparing the size of triangular hitboxes, or for simple polygon analysis.
• Manufacturing and Engineering: Cutting materials into triangular shapes, where comparing areas helps minimize waste or determine material requirements.
• Educational Software: Developing interactive tools for students to visualize and compare geometric properties of triangles.

Solution Approaches

We will explore two primary approaches for calculating triangle areas and then comparing them:

1. Using Base and Height: The most straightforward method, ideal when these dimensions are readily available.
2. Using Heron's Formula (Three Sides): A more general approach, useful when only the side lengths of the triangles are known.

Approach 1: Comparing Triangles Using Base and Height

This approach calculates the area of each triangle using the classic 0.5 * base * height formula and then compares the results.

• Summary: Input base and height for two triangles, calculate their areas, and compare them.
• Code Example:

// Compare Triangle Areas (Base & Height)
#include <stdio.h>

int main() {
    float base1, height1, base2, height2;
    float area1, area2;

    // Step 1: Get dimensions for Triangle 1
    printf("Enter base for Triangle 1: ");
    scanf("%f", &base1);
    printf("Enter height for Triangle 1: ");
    scanf("%f", &height1);

    // Step 2: Get dimensions for Triangle 2
    printf("Enter base for Triangle 2: ");
    scanf("%f", &base2);
    printf("Enter height for Triangle 2: ");
    scanf("%f", &height2);

    // Step 3: Calculate areas
    area1 = 0.5 * base1 * height1;
    area2 = 0.5 * base2 * height2;

    // Step 4: Display calculated areas
    printf("\\nTriangle 1 Area: %.2f\\n", area1);
    printf("Triangle 2 Area: %.2f\\n", area2);

    // Step 5: Compare areas and display the result
    if (area1 > area2) {
        printf("Triangle 1 is greater than Triangle 2.\\n");
    } else if (area2 > area1) {
        printf("Triangle 2 is greater than Triangle 1.\\n");
    } else {
        printf("Both triangles have equal areas.\\n");
    }

    return 0;
}

Run

• Sample Output:

Enter base for Triangle 1: 10
Enter height for Triangle 1: 5
Enter base for Triangle 2: 8
Enter height for Triangle 2: 7

Triangle 1 Area: 25.00
Triangle 2 Area: 28.00
Triangle 2 is greater than Triangle 1.

• Stepwise Explanation:

1. Declare four float variables (base1, height1, base2, height2) to store the dimensions of the two triangles, and two more float variables (area1, area2) for their respective areas.
2. Prompt the user to input the base and height for both Triangle 1 and Triangle 2 using printf and store the values using scanf.
3. Calculate area1 using the formula 0.5 * base1 * height1 and area2 using 0.5 * base2 * height2.
4. Print the calculated areas for both triangles, formatted to two decimal places.
5. Use an if-else if-else structure to compare area1 and area2. The program then prints a message indicating which triangle has a larger area or if their areas are equal.

Approach 2: Comparing Triangles Using Heron's Formula

Heron's formula allows you to calculate the area of a triangle given the lengths of its three sides. This approach also includes a check to ensure that the given side lengths can form a valid triangle.

• Summary: Input three side lengths for two triangles, validate them, calculate areas using Heron's formula, and compare.
• Code Example:

// Compare Triangle Areas (Heron's Formula)
#include <stdio.h>
#include <math.h> // Required for sqrt()

// Function to calculate area using Heron's formula
float calculateTriangleArea(float a, float b, float c) {
    // Check for valid triangle (Triangle Inequality Theorem)
    if (a + b > c && a + c > b && b + c > a) {
        float s = (a + b + c) / 2; // Semi-perimeter
        return sqrt(s * (s - a) * (s - b) * (s - c));
    } else {
        return -1.0; // Indicate an invalid triangle
    }
}

int main() {
    float a1, b1, c1; // Sides for Triangle 1
    float a2, b2, c2; // Sides for Triangle 2
    float area1, area2;

    // Step 1: Get dimensions for Triangle 1
    printf("Enter side 1 for Triangle 1: ");
    scanf("%f", &a1);
    printf("Enter side 2 for Triangle 1: ");
    scanf("%f", &b1);
    printf("Enter side 3 for Triangle 1: ");
    scanf("%f", &c1);

    // Step 2: Get dimensions for Triangle 2
    printf("Enter side 1 for Triangle 2: ");
    scanf("%f", &a2);
    printf("Enter side 2 for Triangle 2: ");
    scanf("%f", &b2);
    printf("Enter side 3 for Triangle 2: ");
f    scanf("%f", &c2);

    // Step 3: Calculate areas using the function
    area1 = calculateTriangleArea(a1, b1, c1);
    area2 = calculateTriangleArea(a2, b2, c2);

    // Step 4: Display calculated areas and comparison
    if (area1 == -1.0) {
        printf("\\nInvalid sides for Triangle 1. Cannot calculate area.\\n");
    } else {
        printf("\\nTriangle 1 Area: %.2f\\n", area1);
    }

    if (area2 == -1.0) {
        printf("Invalid sides for Triangle 2. Cannot calculate area.\\n");
    } else {
        printf("Triangle 2 Area: %.2f\\n", area2);
    }

    if (area1 != -1.0 && area2 != -1.0) { // Only compare if both are valid
        if (area1 > area2) {
            printf("Triangle 1 is greater than Triangle 2.\\n");
        } else if (area2 > area1) {
            printf("Triangle 2 is greater than Triangle 1.\\n");
        } else {
            printf("Both triangles have equal areas.\\n");
        }
    } else {
        printf("Comparison cannot be made due to invalid triangle(s).\\n");
    }

    return 0;
}

Run

• Sample Output 1 (Valid Triangles):

Enter side 1 for Triangle 1: 3
Enter side 2 for Triangle 1: 4
Enter side 3 for Triangle 1: 5
Enter side 1 for Triangle 2: 5
Enter side 2 for Triangle 2: 12
Enter side 3 for Triangle 2: 13

Triangle 1 Area: 6.00
Triangle 2 Area: 30.00
Triangle 2 is greater than Triangle 1.

• Sample Output 2 (Invalid Triangle):

Enter side 1 for Triangle 1: 1
Enter side 2 for Triangle 1: 2
Enter side 3 for Triangle 1: 10
Enter side 1 for Triangle 2: 3
Enter side 2 for Triangle 2: 4
Enter side 3 for Triangle 2: 5

Invalid sides for Triangle 1. Cannot calculate area.
Triangle 2 Area: 6.00
Comparison cannot be made due to invalid triangle(s).

• Stepwise Explanation:

1. Include stdio.h for I/O and math.h for the sqrt() function.
2. Define a helper function calculateTriangleArea(float a, float b, float c):

• It first checks the Triangle Inequality Theorem: a + b > c, a + c > b, and b + c > a. If these conditions are not met, the sides cannot form a valid triangle, and the function returns -1.0 to indicate an error.
• If valid, it calculates the semi-perimeter s = (a + b + c) / 2.
• Then, it applies Heron's formula: sqrt(s * (s - a) * (s - b) * (s - c)) and returns the result.

1. In main(), declare float variables for the three sides of each triangle (a1, b1, c1, a2, b2, c2).
2. Prompt the user to input the three side lengths for both Triangle 1 and Triangle 2.
3. Call calculateTriangleArea() for each triangle, storing the results in area1 and area2.
4. Check if area1 or area2 is -1.0. If so, print an error message about the invalid triangle. Otherwise, print the calculated area.
5. Finally, perform the comparison only if both area1 and area2 are valid (not -1.0). Use an if-else if-else block to determine and print which triangle has a larger area or if they are equal. If one or both are invalid, print a message indicating that comparison cannot be made.

Conclusion

We have explored two effective methods to compare the areas of triangles using C programming. The choice between using base and height or Heron's formula depends on the input data available for the triangles. Both approaches demonstrate fundamental programming concepts such as input/output, arithmetic operations, and conditional logic. For Heron's formula, incorporating triangle validity checks is crucial for robust program behavior.

Summary

• Triangle Area (Base & Height):
• Formula: Area = 0.5 * base * height
• Requires: Base and height of the triangle.
• Implementation: Directly calculate and compare.
• Triangle Area (Heron's Formula):
• Formula: s = (a + b + c) / 2, Area = sqrt(s * (s - a) * (s - b) * (s - c))
• Requires: Three side lengths (a, b, c).
• Prerequisites: Include math.h for sqrt().
• Important: Validate triangle sides using the Triangle Inequality Theorem (a+b>c, a+c>b, b+c>a) before calculation.
• Comparison Logic: Use if-else if-else statements to determine if Area1 > Area2, Area2 > Area1, or Area1 == Area2.
• Data Types: Use float or double for areas and dimensions to maintain precision.