How to find the shaded area crossed by semi-circle of radius 2 and quarter-circle of radius 4?
Best Answer
The shaded area is shaped from two intersecting circles like an asymmetric lens! in order to find the area of this lens we simply split it in two parts:
$$
\begin{align}
\text{red area} &= \text{area of }\Delta ABC + \text{area of semi-circle} - \text{area of quadrant} \\
&= \tfrac12 \times 21 \times 28 + \tfrac12 \pi \left(\tfrac{35}{2}\right)^2 - \tfrac14 \pi (21)^2 \\
&= 294 + 481.0563 - 346.3606 \\
&= 428.6957
\end{align}
$$
So it looks like you are right and your book is wrong.
Best Answer
The shaded area is shaped from two intersecting circles like an asymmetric lens! in order to find the area of this lens we simply split it in two parts: