Q80 of 131 Page 226

Rani bought a new field that is next to one she already owns (Fig. 9.34). 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.

(i) Find the perimeter of the lawn.


(ii) Find the area of the square field excluding the lawn.


Given, side of the square = 70 m


Diameter of the semicircular lawn = side of the square = 70 m


∴ Radius = × 70 = 35 m


We know that circumference C of a circle of radius r, is C = 2πr


Perimeter of a semicircle = × 2πr + 2r = πr + 2r


i) So, perimeter of the lawn = × 35 + 2 × 35 = 110 + 70 = 180 m


ii) Area of square = (side)2 = (70)2 = 4900 m2


Area of semicircular lawn = × πr2 = × × (35)2 = 11 × 5 × 35 = 1925 m2


Area of the square field excluding the lawn = Area of square - Area of semicircular lawn


= 4900- 1925 = 2975 m2


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