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.

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!
Area of square with side x = x^2
Diagonal of square =
Half product of diagonals =
=x^2
Proved
Answer by ikleyn(52780)   (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.


RELATED QUESTIONS

show that the area of a square is half the product of its... (answered by jim_thompson5910)
If the area of a square is 4 meter square then what is the length of its diagonals? (answered by TimothyLamb)
how would the area of a kite be affected if its diagonals are half? (answered by ikleyn)
The perimeter of a rectangle is 34 inches, and its area is 60 square inches. What is the... (answered by ankor@dixie-net.com)
The area A of a rhombus is one-half the product of the diagonals p and... (answered by Fombitz)
Prove the following theorem: If the diagonals of a convex quadrilateral are... (answered by jim_thompson5910)
The area of a square is 900 square feet. Find the length of each of its... (answered by sealy123)
show that the diagonals of a square are equal and bisect each other... (answered by MathLover1)
What is the area of a square in square feet, if each of its diagonals is 4 feet... (answered by Boreal)