The problem: prove that the crescent-moon shaped region, upper left, has the same area as the shaded triangle.
Mariama Bah, Shannon Bradley, and Sharif Quansah all handed in correct solutions and won prizes.
Proof: Let AO be 1 unit. Then the area of the triangle is ½ unit, and AB is √2 units, by Pythagoras.
The area of the semicircle ABC is 2π
The area of the quarter-circle AFBO is π
The area of the segment AFBD is π−½
The area of the semicircle AEB is π
The area of the crescent-shape = area of semicircle AEB minus area of segment AFBD
=area of triangle ∎