2020 · Q91
What is the area of the shaded region in the given figure, if the radius of each of the circles is 2 cm?
Elementary MathematicsCircles
- A4√3 − 2π cm²
- B√3 − π cm²
- C√3 − π/2 cm²
- D2π − 2√3 cm²
Explanation
The three centres form an equilateral triangle of side 4 (area 4√3), from which three 60° sectors (together a half-circle of radius 2, area 2π) are removed. The gap area is 4√3 − 2π. The three 60° sectors together make exactly a half-circle of radius 2.