How do I find the area of this region?

A square with edge length 2 cm has semicircles drawn on each side.
Find the total area of the shaded region.

Here is an image of the diagram shown :

Please show your work in pictures, numbers, words, anything. (Try to keep it to a Grade 8 level too)

The square has area $4$.

The top and bottom white region together have area $4$ minus $2$ times the area of the semi circle, that is, $4-2\times \pi r^2/2=4-\pi$ (since $r=1$).

So, dividing by $2$, the top blue region has area $2-\pi/2$.

If you remove this area from the area of the top semi circle you obtain the area of the two top red parts.

Double it to obtain the red area.

Move one half of a leaf to the circle:

$\hspace{3cm}$

The area of the quarter circle is $\frac\pi4$; the area of the triangle is $\frac12$. Thus, the area of the half-leaf (in red) is $\frac\pi4-\frac12$. There are two per leaf, therefore the area of four leaves is $$ 8\left(\frac\pi4-\frac12\right)=2\pi-4 $$