Sum of the Area of Lunes

on the

Legs of a Right Triangle

A lune is a plane figure bounded by the arcs of two circles. As a planar figure, the lune has an area but determining the area may be a challenge.

It is well known that a square with the same area as a circle can not be constructed with straightedge and compass. Surprisingly, even though the lune is bounded by arcs of circles, some lunar shapes can be shown to have a constructable square of the same area.

## On a Right Triangle