It is actually very simple problem. All we need to do is find the area of rectangle inside it and then subtract that area from the area of semi circle.
First we wound area of rectangle:
[tex]A_r=ab=16\cdot6=96[/tex]
We need to ask ourselves how to find a radius?
First we split rectangle in 2 rectangle. A diagonal of 1 rectangle is the radius [tex]d=r[/tex]. The rectangle has length of 8 and width of 6. So the diagonal is,
[tex]d=\sqrt{l^2+w^2}=\sqrt{8^2+6^2}=10[/tex]
We find our radius is 10.
Then we find area of semicircle which is area of circle divided by 2.
[tex]A_s=\dfrac{\pi r^2}{2}=\dfrac{10\pi}{2}=5\pi[/tex]
And finally the shaded area,
[tex]A=A_r-A_s=96-15\pi=\boxed{48.88}[/tex]
Hope this helps.
r3t40
