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The square ABCD has a side length of 1, and AEF is an equilateral triangle. What is the area of AEF?

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The square ABCD has a side length of 1, and AEF is an equilateral triangle. What is the area of AEF?

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posted Apr 1, 2020 by Pardeep Kohli

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1 Answer

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2sqrt(3)-3


Area=sqrt(3)/4* a^2, where a= side of equilateral triangle


BE=x --> EC=1-x --> CF=1-x, FD=x
From triangle ABE ---> a^2 = 1+x^2
From triangle ECF ---> a^2 = 2*(1-x)^2
1+x^2=2x^2-4x+2 -> x^2-4x+1=0 -> x=2-sqrt(3) --> a^2=x^2+1=8-4sqrt(3)
A=sqrt(3)/4*a^2=sqrt(3)/4*(8-4sqrt(3))=2sqrt(3)-3

answer Apr 19, 2020 by Hanifa Mammadov



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