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Question
The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.
Solution
Let the radius of the park be r.
Length of chain = Perimeter of the semicircular park
⇒ 108 = Length of the arc +Diameter
`=> 108 = 1/2xx2pi"r" + 2"r"`
`⇒ 108 = r (22/7+2) `
`=> 108 = 36/7"r"`
⇒ r = 21 m
Now, Area of park` = 1/2pi"r"^2 = 1/2xx22/7xx(21)^2 = 693 "m"^2`
Hence, the area of the park is 693 m2 .
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