Math CentralQuandaries & Queries


Question from Brian, a student:

How do you figure out the area of an equilateral triangle with only the clue of a regular hexagon perfectly inside it (no boarders) and the only thing you know about the hexagon is it has an area of 12cm^2?

Hi Brian.

A hexagon can be subdivided into 6 congruent equilateral triangles. Draw this.

You will quickly see that due to symmetry, the equilateral triangle extrudes 3 additional congruent triangles to 3 of the hexagon's sides.

Thus, the area of the triangle is 9/6 the area of the hexagon.

Stephen La Rocque.

PS: Here is the logo from the 1967 Canadian Centennial celebration.

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