Math CentralQuandaries & Queries


Question from Siddharth, a student:

When 2 congruent equilateral triangles share a common center, their union can be a star
If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?

a) 60 b) 70 c) 80 d)90 e)100

Please provide an explanation if you can, based on the answer.


Hi Siddharth. Let's draw this with the diameters across the corners of the hexagon.


Do you see any other congruent triangles besides the two big equilateral triangles? Count them up and use ratios to determine the answer to your question.


PS: 1967 was Canada's centennial year (Math Central is operating from Canada). The logo we chose was very much like the diagram above changed slightly to resemble a maple leaf, our national symbol on our flag:


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