Overlapping Equilateral Triangles

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?

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△ABC and △DEF create hexagon UVWXYZ.

△ABC has area 24 cm2. 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

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