There are a few ways to go about doing this, but the easiest is portably to break it up into three shapes: two identical triangles, and a rectangle. The area of one triangle is:
1/2 (10x8) = 40, so the area of two triangles is 80.
The area of the square is 20 x 8, which is 160.
The total area is the sum of the two:
80 + 160 = 240, and this is your total area.