What is the total area of this composite figure rounded to the nearest inch?

So basically what we have here is a rectangle on the bottom part, and then a half circle on the upper part. We'll need to add these two areas together to get the total area.

For the area of the rectangle, simply multiply 6 in times 2 in (base times height), giving you $12\; in^2$.

For the half circle, we know that the area of a circle is pi times the radius^2. Well, we don't know the radius but we do know the diameter of this circle, which is 6 in. The radius is always half the diameter, so the radius is 3 in.

Meaning, the area of this half circle is 1/2(pi((3 in)^2)) =

$\frac{9}{2}\pi\; in^2$

or aproximately 

$14.13\; in^2$

Adding these together we get aproximately

$28.13\; in^2$

Which, if we're rounding to the nearest inch, would come out to

$28\; in^2$

Thanks for the question dude. If you have any additional questions or don't understand how I did this, or even see a mistake of mine, feel free to let us know and me or another forum member would love to help!

NinjaDevo's METHODOLOGY is correct, bu there is an error in the CALCULATION 

9/2 pi = 14.137      TRUE !

Now add 12         14.137 + 12 = 26.137   ~=26       NOT  28   !