Question

$△ABC$ is an equilateral triangle. If each sector at the three vertices is of radius $rcm$, calculate the total area of the sectors.

• A. $\frac{1}{4}\pi r^2$
• B. $\frac{7}{2}\pi r^2$
• C. $2\pi r^2$
• D. $\frac{1}{2}\pi r^2$

Answer 1

The correct option is D $\frac{1}{2}\pi r^2$

Total area of three sectors = $3\times \frac{\theta }{{360}^0}\times \pi r^2=3\times \frac{{60}^0}{{360}^0}\times \pi r^2=\frac{1}{2}\pi r^2$