A polygon with an area of 75 is described around a circle with an area of 25pi. Find the perimeter of this polygon.
| February 11, 2021 | education
The universal formula for finding the area of any described polygon is:
S = r * п, where r is the radius of the inscribed circle and p is a semiperimeter.
p = S / r.
Find r = √ (25 п / п) = 5.
p = 75/5 = 15.
Thus, the full perimeter is P = 15 * 2 = 30.
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