Question

In Figure-8, ABCD is a parallelogram. A semicircle with centre O and the
diameter AB has been drawn and it passes through D. If
AB = 12 cm and OD 1 AB, then find the area of the shaded region
(Use n = 314)
(93-7
Figure-8​

Answer 1

In Figure-8, ABCD is a parallelogram. A semicircle with centre O and the diameter AB has been drawn and it passes through D. When AB = 12 cm and OD 1 AB, then the area of the shaded region is 7.74 cm^2.

Given,

AB = 12 cm

OA = OB = OD = AB/2

= 12/2 = 6cm

Area of shaded portion = Area of parallelogram - Area of quadrant

Area of shaded portion = b × h - (pi × r^2) / 4

= OB × OD - 3.14 × OD^2/4

= 6 × 6 - 3.14 × 6^2/4

= 36 - 28.26

= 7.74 cm^2