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.

1. Find the perimeter of the lawn.
2. Find the area of the square field excluding the lawn.

Answer 1

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