What is the area of a square whose diagonals are 12?

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Answer 1 · 2017-05-06T02:32:07

Area = #72 units^2#

A square with diagonals of 12 would have side lengths of #6sqrt2#

As the diagonal of the square would cut the square into a #45^o-45^o-90^o# triangle.

This triangle has a ratio of #1-1-sqrt2#

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Meaning the legs would be #12/sqrt2#

Which is #12/sqrt2(sqrt2/sqrt2)# = #(12sqrt2)/2# = #6sqrt2#

Therefore the square would have sides of #6sqrt2#

Area of the square is #A=s^2#

#A = (6sqrt2)^2#

#A = 36*2#

#A = 72#