Find the Area of the shaded region in the given problem

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chwala

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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
[tex]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)[/tex]
where
[tex]\sin\alpha =\frac{1}{3}[/tex]
Is it same as your idea ?
 
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