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 = }(\theta)/(360^0)\text{ }*\text{ }\pi r^2 \\ =\text{ }(270^0)/(360^0)\text{ }*\text{ }\pi\text{ }*4^2 \\ =\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 }*\text{ 37.7} \\ =\text{ }150.8\text{ square units} \\ =\text{ 151 square units} \end{gathered}`

Answer = 151 square units