Question

Find the area of the shaded region given the radius of each circle is 4. Answer in exact form is preferred.

Answer 1

In each circle, we have a sector that subtends an angle of 270 deg at the center, with a radius of 4

We can obtain the area of each sector as :

$\begin{gathered} \text{Area of sector = }\frac{\theta}{360^0}\text{ }\times\text{ }\pi r^2 \\ =\text{ }\frac{270^0}{360^0}\text{ }\times\text{ }\pi\text{ }\times4^2 \\ =\text{ 37.7 square units} \end{gathered}$

Given that there are 4 of such sectors, we have:

$\begin{gathered} \text{Area of shaded region = 4 }\times\text{ 37.7} \\ =\text{ }150.8\text{ square units} \\ =\text{ 151 square units} \end{gathered}$

Answer = 151 square units