Surface Area and Volume of Hexagonal Prism in C programming

The surface area of any figure is the total area that its surface covers. A hexagonal prism is a three-dimensional figure that has a hexagon at both its ends.

In mathematics, a hexagonal prism is defined as a three-dimensional figure with 8 faces, 18 edges, and 12 vertices. It consists of two hexagonal bases connected by rectangular faces.

Syntax

Surface Area = 6ah + 3?3a²
Volume = (3?3/2)a²h

Where:

• a = side length of the hexagonal base
• h = height of the prism

Example

The following program calculates both surface area and volume of a hexagonal prism −

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

int main() {
    float a = 5.0, h = 10.0;
    
    // Calculate surface area of hexagonal prism
    float surface_area = 6 * a * h + 3 * sqrt(3) * a * a;
    printf("Surface Area: %.2f<br>", surface_area);
    
    // Calculate volume of hexagonal prism
    float volume = 3 * sqrt(3) * a * a * h / 2;
    printf("Volume: %.2f<br>", volume);
    
    return 0;
}

Surface Area: 429.90
Volume: 649.52

How It Works

• Surface Area: Consists of 6 rectangular faces (6ah) plus 2 hexagonal bases (2 × 3?3a²/2 = 3?3a²)
• Volume: Base area (3?3a²/2) multiplied by height (h)
• The sqrt(3) function calculates the square root of 3, which is approximately 1.732

Conclusion

This program demonstrates how to calculate the surface area and volume of a hexagonal prism using mathematical formulas. The surface area includes both the hexagonal bases and rectangular lateral faces, while the volume is the product of the base area and height.