Question

I also need some help on this one. I need the area of the shaded region

Answer 1

What you have is, a circle inside an OCTAgon, OCTA=8 sides

so hmm get the area of the octagon, will include the area also of the circle,
then
get the area of the circle, and subtract it from the area of the octagon
what's left, is the "difference", or the shaded area

$\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}\cdot n\cdot s^2\cdot cot\left( \frac{180}{n} \right)\qquad \begin{cases} n=\textit{number of sides in the polygon}\\ s=\textit{length of one side}\\ \frac{180}{n}=\textit{angle in degrees}\\ ----------\\ n=8\\ s=10 \end{cases}$

$\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad r=radius$

when taking the cotangent, make sure your calculator is in Degree mode, since the angle is in degrees