Okay then:

This one represents square ABCD. Point P is randomly placed randomly within ABCD.

The circular line shown in this picture represents the line on which angle APB will be a right angle. Anything above the line in the white area and angle APB will be obtuse, anything below and angle APB will be acute. And since obviously any point within the square makes angles ABP and PAB acute, if point P is placed anywhere within the gray shaded area than all the angles on triangle PAB will have only acute angles.

So how do we figure this area out?

Well, AB is 1. So, the area of square ABCD is also 1 (A = 1²). The area for the half circle would be ½pi(½)² = ½pi(¼) = pi(

^{1}/

_{8}) =

^{pi}/

_{8}.

Therefore, the area of the gray shaded area would be 1 -

^{pi}/

_{8}!

Hope that makes sense.