The ancient Greeks, being masters of geometric manipulation, often tried their hand at "squaring" various shapes. This involved using only the most fundamental rules of geometry to construct a square whose area equals the area of the original shape.
Can you follow in their footsteps and square a simple triangle?
The solution must hold for all types of triangles.
Let B be the base of the triangle, and H its height. Draw a segment of
length B+H/2; point A is at a distance B from the left. Draw a
semicircle having that segment as its diameter. Draw a perpendicular to
the segment through A. Let C be the intersection of the perpendicular
and the semicircle. AC is the side of a square with equal area.