Given here is a regular decagon, inscribed within a circle of radius r, the task is to find the area of the decagon.
Input: r = 5 Output: 160.144 Input: r = 8 Output: 409.969
We know, side of the decagon within the circle, a = r√(2-2cos36)(Refer here)
So, area of the decagon,
A = 5*a^2*(√5+2√5)/2 = 5 *(r√(2-2cos36))^2*(√5+2√5)/2=(5*r^2*(3-√5)*(√5+2√5))/4
Below is the implementation of the above approach:
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- Area of a circle inscribed in a regular hexagon
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- Find the area of largest circle inscribed in ellipse
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- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
- Program to calculate area of inner circle which passes through center of outer circle and touches its circumference
- The biggest possible circle that can be inscribed in a rectangle
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- Area of largest triangle that can be inscribed within a rectangle
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