Question

Find the area of the shaded portion. Given that each circle is having a radius of $2cm$

• A. $(2\sqrt{3}-\pi )c{m}^2$
• B. $2(2\sqrt{3}-2\pi )c{m}^2$
• C. $2(2\sqrt{3}-\pi )c{m}^2$
• D. $2(2\sqrt{5}-\pi )c{m}^2$

Answer 1

The correct option is C $2(2\sqrt{3}-\pi )c{m}^2$

R.E.F image

As $AC=AB=BC=zr=4$

$\therefore ABC$ is equilateral $△$.

$\Rightarrow \angle A=\angle B=\angle C={60}^o$

$\therefore$ area of shaded port

$=ar\left(ABC\right)-3\times ar\left(ADE\right)$

$=\frac{\sqrt{3}}{4}\times 4^2-3\times \frac{60}{360}\times \left(\pi 2^2\right)$

$=4\sqrt{3}-2\pi$

$=2(2\sqrt{3}-\pi )c{m}^2$