Question

In the following figure, A is the centre of the arc of the circle. Find the perimeter and the area of the shaded region and the side of square is 10 cm.

Answer 1

Side of square = 10 cm

From the figure:

The arc is a semicircle

The diameter of the semicircle = Side of square = 10 cm

Therefore, radius: r = `10/2` = 5 cm

1. Perimeter of shaded region

The boundary consists of:

Bottom of square = 10 cm

Two vertical sides = 10 cm + 10 cm

Semicircular arc

Length of semicircular arc

Arc length = πr

= `22/7 xx 5`

= `110/7`

= 15.71 cm

Total perimeter

= 10 + 10 + 10 + 15.71

= 45.71 cm

2. Area of Shaded Region

Area of shaded region – Area of square + Area of semicircle

Area of square

= 10 × 10

= 100 cm²

Area of semicircle

= `1/2 πr^2`

= `1/2 xx 22/7 xx 5^2`

= `1/2 xx 22/7 xx 25`

= `550/14`

= 39.29 cm²

Total area

= 100 + 39.29

= 139.29 cm²