How do you solve this geometry problem?

Question

the diagonals of a parallellogram are 82 and 30 cm. one altitude is 18 cm long. find the two possible values for the area.

there are no sides and its solvable

Answer 1

There you go, hope it helps:

http://img250.imageshack.us/img250/3518/paralelogramcopynq8.jpg

Any doubts just tell me.

[edit] well, i'll be! I can't sum 80 plus 24 properly! Please follow Northstar's correction. Thanks Northstar!

Answer 2

Ferts has a great diagram and his methodology is correct. He just has a little arithmatic error.

You have two right triangles and when you add the bases together you get twice the length of the parallelogram.

Triangle 1.

y² = 82² - 18² = 6400
y = 80

Triangle 2.

x² = 30² - 18² = 576
x = 24

Let
L = length of parallelogram
A = area of parallelogram
h = altitude of parallelogram

2L = x + y = 80 + 24 = 104
L = 104/2 = 52

A = Lh = 52*18 = 936 cm²

Answer 3

we get a definite value that is are of parallelogram=1008
For further details mail me at [e-mail]
thanks for the 2 points too.