The Rev Dodgson said:

KJW said:

Actually, there is a much simpler approach:

Let D be the diameter of the semicircle, and B be the length of the base of the rectangle. Then:

6/D = B/6 = cosθ (Note that the two triangles (one shown, the other implied) are similar)

Multiply by 6D:

DB = 36

Area = ½ DB = 18

Nice one :)

Shows it works for θ > 45 degrees as well.

How it looks for θ = 60 degrees