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
Attached Figure / Diagram
A
43.36cm2
B
32.072
C
18.212
D
6.932
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36305)