Ineed to find the area of the shaded region

Well first find the area of the semi-circle. 

If the area of a cricle is equal to pi*radius^2 , then you can just find that and divide by 2.

So, A = pi*2^2. = 4pi

We know that the radius is 2 because the length of the side of the rectangle is 4, meaning that the diameter of the semi-circle is 4, and so the radius is 2 as it is half of the diameter. 

We can easily calculate the area of the rectangle, which is
 Length * width = 6*4 = 24.

Next we divide 4pi by 2 in order to get the area of the semi-circle, giving us an area of 2pi

We can just subtract 2pi from 24 and get the area of the shaded region.

Area of the shaded region (answer): 17.7