Two congruent equilateral triangles are placed so that their overlap is a regular hexagon. The triangles each have area 24 sq. cm. What is the area of the hexagon?

△ABC and △DEF create hexagon UVWXYZ.

△ABC has area 24 cm^{2}. It’s composed of nine small triangles, e.g. △AUV.

Each small triangle has area

The hexagon contains six of those triangles, thus its area is