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| Math Central | Quandaries & Queries |
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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.
Cheers,
Stephen La Rocque.
PS: Here is the logo from the 1967 Canadian Centennial celebration.
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