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A regular decagon is a ten sided polygon with all sides and angles equal. And here we need to find the area of a decagon that is inscribed inside a circle using the radius of the circle r,

Mathematical formula for the side of the decagon inscribed in the circle,

a = r√(2-2cos36^{o})

(Using cosine rules)

Formula for finding area of decagon,

Area = 5*a^{2}*(√5+2√5)/2 Area = 5 *(r√(2-2cos36))^^{2}*(√5+2√5)/2 Area = (5r^{2}*(3-√5)*(√5+2√5))/4

Using this formula in a program,

#include <stdio.h> #include <math.h> int main() { float r = 8; float area = (5 * pow(r, 2) * (3 - sqrt(5))* (sqrt(5) + (2 * sqrt(5))))/ 4; printf("area = %f",area); return 0; }

area = 409.968933

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