Find the Area of the shaded region in the given problem

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The discussion revolves around finding the area of a shaded region in a geometry problem, with one participant expressing initial confusion but ultimately arriving at a solution. They reference a textbook answer of 17.5 and plan to double-check their rounding. The participant shares their working formula, which involves calculating areas using trigonometric functions and geometric principles. They seek confirmation on whether their approach aligns with others in the discussion. The conversation highlights the complexity of the problem and the collaborative effort to verify solutions.
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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...
1678364583516.png


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

1678364659756.png

1678364699766.png
 
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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 ?
 
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