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An equilateral triangle with sides 10 inches ,is inscribed in a square ABCD in such a way that one vertex is at A ,another vertex on BC and one on CD . Find the area of square??

An equilateral triangle  with sides 10 inches ,is inscribed in a square ABCD in such a way that one vertex is at A ,another vertex  on BC and one on CD . Find the area of square??
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
3 years ago
thanks for asking. well, first of all draw a figure and name the equilateral triangle as AEF, such that E lies on BC and F on CD. now let angle EAB= y then obviously angle FAD= 30 – y (because angle EAF=60 and angle BAD=90)
now AB=AD
so, 10cosy=10cos(30 – y)
or y=30-y
or y=15
so area of square is (10cosy)^2=100cos^2y=50(1+cos2y)=50(1+root3/2)
=25(2+root3) sq units

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