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Question 666372: The diagonals of square Abcd intersect at point O. If AO=3 what is the area of abcd?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! All diagonals intersect at the center of a square.
Also, the diagonal bisects the angle of the square.
If you were to draw a line from O to the midpoint of A and C (C is in the bottom left corner we have ourselves a 45,45,90 triangle.
Recall that the sides of a 45 45 triangle are a,a,asqrt(2).
well our asqrt(2) = 3 in this case so 3/sqrt(2) = 3sqrt(2)/2 is the length of a.
3sqrt(2)/2 is half the distance of the side of a square, so s = 3sqrt(2)
s^2 = (3sqrt(2))^2 = 9 * 2 = 18.
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