(Q7)ABCD is a rectangle with AB = 14 cm. and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded region.

Given AB = 14cm, AD = BC = 7cm Area of the shaded and unshaded region

= (2× Area of the semi-circles with AD as diameter)+Area of the rectangle

=2 ×
x
360
 ×πr2.θ+l.b

=2×
180°
360°
 ×
22
7
 ×(
2
 )×(
2
 )× θ + ×

=
2
 cm2

Area of unshaded region

=
1
2
 ×
22
7
 ×
2
 ×
2
 = cm2

Area of the shaded region = Total area - Unshaded region

=
2
 -
=
-
2
 =
2
 = .5 cm2