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Question
Rani bought a new field that is next to one she already owns (see figure). This field is in the shape of a square of side 70 m. She makes a semi-circular lawn of maximum area in this field.
- Find the perimeter of the lawn.
- Find the area of the square field excluding the lawn.
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Solution
i. Given, side of a square = 70 m
From the given figure, the diameter of semi-circle is same as the side of a square.
∴ Diameter of semi-circle = 70 m
∴ Diameter of semi-circle = Side of square
∴ Radius = `70/2` = 35 m ...`[∵ "Radius" = "Diameter"/2]`
∴ Perimeter of lawn = πr + 2r
= `22/7` × 35 + 2 × 35
= 110 + 70
= 180 m
ii. Area of square = Side × Side
= 70 × 70
= 4900 m2
∴ Required area = Area of square – Area of semi-circle
= `4900 - 1/2 xx π xx (35)^2` ...`[∵ "Area of semi-circle" = 1/2 πr^2]`
= `4900 - 1/2 xx 22/7 xx 35 xx 35`
= 4900 – 1925
= 2975 m2
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