The perimeter of a regular quadrilateral is 128 cm. Find the area of a circle inscribed in it.
| July 4, 2021 | education
1. Since all sides and angles of a regular polygon are equal to each other, we conclude that the original quadrangle is a square.
2. Find the side of the square by the formula a = P / 4, where P is its perimeter.
a = 128/4 = 32 (cm).
3. Since all sides of the described square are tangents to the inscribed circle, we conclude that the diameter of the original circle is equal to the side of the square.
4. Find the radius of the circle by the formula r = d / 2, where d is its diameter.
r = 32/2 = 16 (cm).
5. Find the area of the circle by the formula S = Pr ^ 2, where П = 3.14.
S = 3.14 × 16 ^ 2 = 3.14 × 256 = 803.84 (cm ^ 2).
Answer: 803.84 (cm ^ 2).
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