Program to calculate area of Enneagon

An enneagon (also known as nonagon) is a polygon with 9 sides. To calculate the area of an enneagon, we use a specific mathematical formula based on the side length.

Syntax

Area = (a² × 9) / (4 × tan(20°))
Area ? 6.1818 × a²

Where a is the length of each side of the enneagon.

Example

The following program calculates the area of an enneagon using the mathematical formula −

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

int main() {
    float side = 6.0;
    float area;
    float multiplier = 6.1818;
    
    printf("Program to find area of Enneagon
");
    printf("The side of the Enneagon is %.1f
", side);
    
    area = multiplier * side * side;
    
    printf("The area of Enneagon is %.2f
", area);
    return 0;
}

Program to find area of Enneagon
The side of the Enneagon is 6.0
The area of Enneagon is 222.65

Key Points

• The multiplier 6.1818 is derived from the formula (9) / (4 × tan(20°))
• The angle 20° comes from dividing 180° by 9 (the number of sides)
• This formula works for any regular enneagon where all sides are equal

Conclusion

Calculating the area of an enneagon is straightforward using the formula 6.1818 × a². This approach provides accurate results for any regular nine-sided polygon.