4310.31 – Star of David

The star of David consists of overlapping congruent equilateral triangles arranged so the overlap is a regular hexagon as in the figure below. If the triangles in this particular star each has area 24 sq. cm., then what is the area of the overlap?



Inspecting the star of David below, we see that the hexagonal overlap consists of 6 equilateral triangles of side xx. Now the area of each of the big equilateral triangles is 24 AND we can see that each consists of 9 equilateral triangles of side xx. Therefore the area of the hexagon is six-ninths the area of one of the big equilateral triangles, i.e., 16.