SOLUTION: Show that the area of a square is half the product of its diagonals. Then consider the possibility that there might be other quadrilaterals with the same property.

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Question 1154771: Show that the area of a square is half the product of its diagonals. Then consider the possibility that there might be other quadrilaterals with the same property.
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Area of square with side x = x^2
Diagonal of square = sqrt%282%29%2Ax
Half product of diagonals = %281%2F2%29%2A%28sqrt%282%29%2Ax%29%5E2
=x^2
Proved

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Any rhombus has the same property.


Any kite has the same property.


Any quadrilateral with the perpendicular diagonals (even if it is NEITHER a kite NOR a rhombus) has the same property.