Program to calculate area and volume of a Tetrahedron

A tetrahedron is a pyramid with a triangular base i.e. it has a base that is a triangle and each side has a triangle. All the three triangles converge to a point. As shown in the figure −

The code to find the area and volume of tetrahedron uses the math library to find the square and square-root of a number using sqrt() and pow() functions. For a regular tetrahedron with side length a, the surface area and volume can be calculated using specific formulas.

Syntax

Surface Area = ?3 * a²
Volume = a³ / (6 * ?2)

Example

This program calculates both the surface area and volume of a regular tetrahedron with a given side length −

#include <stdio.h>
#include <math.h>

int main() {
    int a = 5;
    float area, volume;
    
    printf("Program to find area and volume of Tetrahedron<br>");
    printf("The side of Tetrahedron is %d<br>", a);
    
    // Calculate surface area using formula: ?3 * a²
    area = (sqrt(3) * (a * a));
    printf("The surface area of Tetrahedron is %.6f<br>", area);
    
    // Calculate volume using formula: a³ / (6 * ?2)
    volume = (pow(a, 3) / (6 * sqrt(2)));
    printf("The volume of Tetrahedron is %.6f<br>", volume);
    
    return 0;
}

Program to find area and volume of Tetrahedron
The side of Tetrahedron is 5
The surface area of Tetrahedron is 43.301270
The volume of Tetrahedron is 14.731391

Key Points

• The formulas work only for regular tetrahedrons where all edges have the same length.
• The math.h library is required for sqrt() and pow() functions.
• Surface area represents the total area of all four triangular faces.

Conclusion

Calculating the area and volume of a regular tetrahedron involves applying mathematical formulas using the sqrt() and pow() functions from the math library. These calculations are essential in geometry and 3D modeling applications.