Done
Hello,
the shaded area can be calculated by:
area of sector - area of right triangle
The angle(ROP) = $\displaystyle \frac{3 \pi}{16}$
Thus the area of the sector is: $\displaystyle \frac{A_{sector}}{\pi r^2}=\frac{\frac{3 \pi}{16}}{2\pi} \ \Longleftrightarrow \ A_{sector}=\frac{3}{32} \pi r^2$
The area of the right triangle is $\displaystyle A_{\text{right triangle}}=\frac{1}{2} \cdot {base} \cdot {height}$
If r is the length of the radius (here r = 4 cm) then the length of the base:$\displaystyle b=r \cdot \cos \left(\frac{3 \pi}{16} \right)$ and
the length of the height is: $\displaystyle h=r \cdot \sin \left(\frac{3 \pi}{16} \right)$
Therefore the shaded area is:
$\displaystyle A_{\text{shaded area}}=\frac{3}{32} \pi r^2 - \frac{1}{2} \cdot r \cdot \cos \left(\frac{3 \pi}{16} \right) \cdot r \cdot \sin \left(\frac{3 \pi}{16} \right)$
Plug in the values you know to calculate the area.
(For confirmation only: I've got A = 1.017 cm²)