Question

Rani bought a new field that is next to one she already owns in the given 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 = ${\displaystyle \frac{70}{2}}$ = 35 m  .....${\displaystyle [\because \text{Radius}=\frac{\text{Diameter}}{2}]}$

∴ Perimeter of lawn = πr + 2r

= ${\displaystyle \frac{22}{7}}$ × 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

= ${\displaystyle 4900-\frac{1}{2}\times \pi \times {\left(35\right)}^2}$ .....${\displaystyle [\because \text{Area of semicircle}=\frac{1}{2}\pi r^2]}$

= ${\displaystyle 4900-\frac{1}{2}\times \frac{22}{7}\times 35\times 35}$

= 4900 – 1925

= 2975 m²