Find the Area of the shaded region in the given problem

[chwala]

Homework Statement

See attached

Relevant Equations

Circular measure

Wawawawawa boggled me a little bit... but finally managed it...seeking alternative approach guys;

kindly note that what i have indicated as $*$ and a $√$ is the correct working ...

Text book answer indicates $17.5$ as answer... will re check my rounding solutions later...

My working- allow me to copy paste here...will later type the working...

 

[anuttarasammyak]

From your sketch, say S is area we want, it seems
$$2S=\frac{1}{2}*20^2 (4\alpha)-4*\frac{1}{2}*15\cos \alpha*5-2*\frac{1}{2}*5^2(\pi+2\alpha)$$
where
$$\sin\alpha =\frac{1}{3}$$
Is it same as your idea ?