Question

In the following figure, If ABC is an equilateral triangle, then shaded area is equal to

(a) $\left(\frac{\mathrm{\pi }}{3}-\frac{\sqrt{3}}{4}\right)r^2$

(b) $\left(\frac{\mathrm{\pi }}{3}-\frac{\sqrt{3}}{2}\right)r^2$

(c) $\left(\frac{\mathrm{\pi }}{3}+\frac{\sqrt{3}}{4}\right)r^2$

(d) $\left(\frac{\mathrm{\pi }}{3}+\sqrt{3}\right)r^2$

Figure

Answer 1

We have given that ABC is an equilateral triangle.

As we know that,.

Area of the shaded region = area of the segment BC.

Let

Substituting the values we get,

Substituting and we get,

Therefore, area of the shaded region is . Hence, the correct answer is option (a).