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: C
Explanation
Area of shaded portion = Area of semicircle Area of \(\bigtriangleup\) RSO Area of semicircle = \(\frac {\pi r^2}{2} = \frac{22\times 4 \times 4}{7 \times 3}\) = 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
