Question

Please don't write random texts. Please answer this question.​

Answer 1

Answer:

The answer is $\dfrac{25\pi}{4}-12$

Step-by-step explanation:

Since ORSQ is a rectangle so diagonal of this rectangle is same as the radius of the semicircle. Let radius be $r$ $\Rightarrow \text{OR}=r-1$

In rectangle ORSQ, we can use Pythagoras                    

               $\Rightarrow \text{OS}^2=\text{OQ}^2+\text{OR}^2\\\Rightarrow r^2=3^2+(r-1)^2\\\Rightarrow r^2=9+r^2-2r+1\\\Rightarrow 2r=10\Rightarrow r=5$

Therefore required shaded area

          $=$ area of quadrant OTP $-$ area of rectangle ORST

          $\displaystyle =\frac{\pi}{4}(5)^2-3\times (5-1)\\\\\\=\frac{25\pi}{4}-12$