Question

Find the area of the shaded segments. Leave your answer in terms of pi or round to the nearest 10th.

Answer 1

Given:

The radius of the circle is 2. and the sector angle is 90 degrees.

The area of the sector is calculated as,

$\begin{gathered} A_S=\frac{\theta}{360^{\circ}}\pi\times r^2 \\ A_S=\frac{90^{\circ}}{360^{\circ}}\times\pi\times2^2 \\ A_S=\pi \end{gathered}$

Now, find the area of the triangle. Whose height and the base are 2 units.

$\begin{gathered} A_T=\frac{1}{2}\times h\times b \\ A_T=\frac{1}{2}\times2\times2 \\ A_T=2 \end{gathered}$

So, the area of the shaded region is,

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