Find the area of shaded region in terms of x.

Answer :

Given side length of square  =  Diameter of semicircle =  4 x 

So,

Radius of semicircle  = 2 x 

And we know area of square  = ( Side )²

So,

Area of given square  =  ( 4 x )² =  16 x²

And we know area of semicircle  = $\frac{\mathrm{\pi } {\mathrm{r}}^2}{2}$
So ,

Area of both semicircles  = $2 \times \frac{{\displaystyle \frac{22}{7}} \times {\left(2x\right)}^2}{2} =\frac{22}{7} \times 4x^2 =\frac{22}{7} \times 4x^2 = \frac{88}{7}{x}^2 = \mathbf{12}\mathbf{.}\mathbf{57}\mathbf{ }{\mathit{x}}^{\mathbf{2}}$
Therefore ,

Area of shaded region  =  16 x² - 12.57 x² = 3.43x²                                                      ( Ans )