In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4cm. Find the area of the shaded region

In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4cm. Find the area of the shaded region

A.

43.36cm2

B.

32.072

C.

18.212

D.

6.932

Correct answer is C

Area of shaded portion = Area of semicircle

Area of \(\bigtriangleup\) RSO

Area of semicircle = \(\frac {\pi r^2}{2} = \frac{22\times 4 \times 4}{7 \times 2}\)

= 25.14cm2; Area of \(\bigtriangleup\)RSO

=\(\sqrt{s(s - 1)(s - b)(s - c)}\); where

s = \(\frac{a + b + c}{2}\)

s = \(\frac{4 + 4 + 4}{2}\)

= 6cm

= \(\sqrt{6(6 - 4)(6 - 4) (6 - 4)}\)

= \(\sqrt{6(2) (2) (2)}\)

= \(\sqrt{18}\) = 6.93cm2

Area of shaded region

= 25.14 - 6.93

= 18.21cm2