To find the area of the shaded area, we need to find the area of the whole circle. To do so we need to find the radius. Looking at the triangle, we know that the top two legs are 4 cm. To find the diameter we can use a^2 + b^2 = c^2.
4^2 + 4^2 = c^2
32 = c^d
c = sqrt(32) or 5.6569... Radius is half of this so r = 2.828
Area of the whole circle is pi* 2.828^2 = 8pi
Now we need to subtract the area of the semi circle and triangle. The semi circle is half the total and the triangle is 0.5bh = 4*4*0.5 = 8
The shaded area is 4.566 cm^2