Lets break this down into recognizable shapes (see the figure below). We see we have a semicircle, one square, and a trapezoid. We can find the area of each, then add them all together.
Area of a circle = pi*r^2
pi*2^2
=4pi
We have to remember that this is a semicircle, so we'll divide by two to get 2pi.
Area of a square = s^2
In this case, s=4, so 4^2 = 16
Area of a trapezoid = 1/2(b1+b2)h, where b1 and b2 are bases.
1/2(8+4)(4) = 24
24+16+2pi = (2pi+40) mm^2
:)
