In the diagram, O is the centre of the circle and PQ is a diameter….

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

Correct Answer: Option C

Explanation

Area of shaded portion = Area of semicircle
Area of (bigtriangleup) RSO
Area of semicircle = (frac {pi r^2}{2} = frac{22times 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