Question

AD is the diameter of a circle of radius 6 centimetre and AB=AC=CD semi circles are drawn with AB and BD as diameter as shown in the figure. Find the perimeter and area of shaded region.

Answer 1

Given :
AD is diameter of circle
AB = BC = CD

Since AD is 6 cm, sum of AB, BC and CD will also be 6.

→ AB=BC=CD = 2cm

Let radius of semicircle with diameter AD be r = 3cm

Let radius of semicircle with diameter AB be x = 2cm

Let radius of semicircle with diameter BD be y = 4 cm ( BC+CD = 2+2 = 4)

Perimeter of the shaded region = perimeter of semi circle with diameter AD and + perimeter of semicircle with diameter BD + perimeter of semicircle with diameter AB.

Perimeter of semicircle = 1/2(2πr) = πr

Perimeter of shaded region :-

πr + πx + πy

→ π(r+x+y)
→ 3.14×(3+2+4)
→3.14 × 9
→ 28.26 cm

Answer :- The perimeter of shaded region is 28.26 cm