The area of the square is 16 sq. units. A semicircle is inscribed on a side of the square with its diameter being that side of the square. An equilateral triangle rests with its base, on the opposite side of the square. Find the intersection area of the semicircle and the equilateral triangle.
I was able to figure out a solution using coordinate geometry. But I want a solution without using it. (Also with minimal usage of trigonometry if possible). Please give a numerical answer.