An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

Correct result:

S =  0.4641

Solution:

a2=12+x2 a2=(1x)2+(1x)2  1+x2=(1x)2+(1x)2  12+x2=(1x)2+(1x)2  12+0.2679491924312=(10.267949192431)2+(10.267949192431)2  0<x<1 x=x2=0.26790.2679  a=1+x2=1+0.267921.0353  S=34 a2=34 1.03532=0.4641

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