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GRE
GRE Quantitative Reasoning Section

Area of a Regular Decagon Inscribed in a Circle

Very Hard Geometry Polygons

Consider a regular polygon with $n$ sides inscribed in a circle of radius $r$. Each vertex of the polygon touches the circle. If the area of this polygon is given by the formula:

$A = \f\frac{1}{2} n r^2 \sin\left(\f\frac{2\pi}{n}\right)$

What is the area of a regular decagon (10-sided polygon) inscribed in a circle with a radius of 5 cm? Use $\sin(\f\frac{2\pi}{10}) = \sin(\f\frac{\pi}{5}) \approx 0.5878$.

Hint

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