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 square inscribed in a circle which is inscribed in a hexagon
- Area of the circle that has a square and a circle inscribed in it
- Area of circle inscribed within rhombus
- Area of circle which is inscribed in equilateral triangle
- Area of a circle inscribed in a regular hexagon
- Find the area of largest circle inscribed in ellipse
- Program to calculate area of an Circle inscribed in a Square
- Find area of the larger circle when radius of the smaller circle and difference in the area is given
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- 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
- Radius of the inscribed circle within three tangent circles
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