Area of Incircle of a Right Angled Triangle in C Program?

To find the area of the incircle (inscribed circle) of a right angled triangle, we use the formula for the inradius and then calculate the area. The inradius r of a right angled triangle is given by r = (P + B − H) / 2, where P is the perpendicular, B is the base, and H is the hypotenuse.

The area of a circle is given by Area = ?*r², where ? = 3.14159 and r is the radius of the circle.

Syntax

Area = ? * ((P + B - H) / 2)²
where P = perpendicular, B = base, H = hypotenuse

Example

This program calculates the area of the incircle for a right triangle with sides 3, 4, and 5 −

#include <stdio.h>
#define PI 3.14159265

int main() {
    float area, P = 3, B = 4, H = 5;
    float radius = (P + B - H) / 2;
    
    printf("Right triangle sides: P=%.1f, B=%.1f, H=%.1f<br>", P, B, H);
    printf("Inradius: %.2f<br>", radius);
    
    area = PI * radius * radius;
    printf("Area of incircle: %.6f<br>", area);
    
    return 0;
}

Right triangle sides: P=3.0, B=4.0, H=5.0
Inradius: 1.00
Area of incircle: 3.141593

Key Points

• The inradius formula r = (P + B − H) / 2 only works for right triangles
• For a 3-4-5 triangle, the inradius is 1 unit
• The area calculation uses the standard circle area formula ?*r²

Conclusion

The incircle area of a right triangle can be efficiently calculated using the inradius formula combined with the circle area formula. This method works for any right triangle given its three sides.