Question

the given figure, PSR, RTQ and PAQ are three semicircles of
diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of
shaded region. [Use = 3.14.]
[CBSE 2014]
7 cm
3 cm​

Answer 1

The perimeter of the shaded region is 31.4 cm.

The perimeter of the shaded region is=

length of the bigger curve + length of the curve inside + length of the curve below.

Therefore,

Circumference of the outer curve = 3.14 x (10/2)

Circumference of the inner curve = 3.14 x (7/2)

Circumference of the curve below = 3.14 x (3/2)

Using Formula for the circumference of the circle,

Perimeter = 3.14 x 5 + 3.14 x 3.5 + 3.14 x 1.5

= 3.14 (5 + 3.5 + 1.5)

=3.14 (10)

= 31.4 cm