A 6 pointed star - Math Central

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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.

Thanks

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

star

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.

Cheers,
Stephen

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:

flag

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.