What you should do for any composite figure is divide it up into smaller parts. We can divide this figure into two parts, the semicircle at the top, and the rectangle at the bottom.
We can find the area of the rectangle easily, it is just 8*10 = 80.
Now to find the area of the semicircle. In case you didn't know, the formula for the area of a circle is π r^2. The r in this case will be 4, because it is half of the diameter, 8. Plug this into the formula to get:
= π (4)^2
Dont forget to divide by 2, because it is a semicircle.
Now, we add the rectangle and the semicircle's area together to get 80 + 8π.
If you want it in decimal form, it is 105.1327412