Question 34
Mensuration of Plane ShapesFind the area of the shaded portion of the semi-circular figure above.
- A.r2/4 (4π − 3√3)
- B.r2/4 (2π − 3√3)
- C.½r2π
- D.⅛r2√3
- E.r2/8 (4π + 3√3)
Show the answer and explanation
Answer: B (r2/4 (2π − 3√3))
Explanation
The semicircle is three 60° sectors, each minus an equilateral triangle. Each segment is πr²/6 − (√3/4)r², so three of them give r²/4(2π − 3√3).