In a circular park of diameter 80 m, there is a square-shaped playground of…
2018
In a circular park of diameter 80 m, there is a square-shaped playground of maximum area. The area of the playground is
- A.
6400 m²
- B.
1600 m²
- C.
3200 m²
- D.
12800 m²
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Correct answer: C
The largest square that can fit inside a circle has its diagonal equal to the diameter of the circle.
Given the diameter is 80 m, the diagonal of the square is 80 m.
The area of a square in terms of its diagonal is given by:
Area = d² / 2 = 80² / 2 = 6400 / 2 = 3200 m².
Therefore, the area of the playground is 3200 m².