What is the area of the shaded part in square centimeter The circle is inscribed in a square with sides 8 cm. What is the area of the shaded part in square centimeters? Express your answer in terms of $\pi$

A nice geometry problem, It's just for sharing a new ideas, thanks:)

Notice, radius of inscribed circle $$=\frac{\text{side of square}}{2}=\frac{8}{2}=4\ cm$$
Area of shaded part $$=\text{(area of semi-circle with radius}\ 4 \ cm)-\text{(area of isosceles triangle)}$$ $$=\frac{1}{2}\pi (4)^2-\frac{1}{2}(2)(8)$$$$=8\pi-8=8(\pi-1)\approx 17.13274123 \ cm^2$$ $$\bbox[5px, border:2px solid #C0A000]{\color{red}{\text{Area of shaded portion}=8(\pi-1)\approx 17.13274123\ cm^2}}$$
