# find shortest length of a isosceles trapezoid

Im not sure if this question is easy or not, the concept of what I'm asking seems simple but I cant figure it out.

Given that A0 = 100, and h = 10, how would I calculate Az.

I have begun by trying to calculate 'x' and then obtain the slope from this but I dont know if I'm over complicating the situation. Can anyone suggest a method for this?

-
The best you can do is write $AZ=100-2x$. Are you trying to find the minimum value of the perimeter of such a trapezoid? If so, note the length of the left/right side is, by the Pythagorean Theorem, $\sqrt{10^2+x^2}$. – David Mitra Jan 10 '13 at 15:44
What keeps $Az$ from being zero (or arbitrarily close to it)? You need more information. – Ross Millikan Jan 10 '13 at 16:05
Thanks for your comments. I am trying to calculate the volume of water in a theoretical lake where as h (the lake depth) increases Az decreases (assuming a conical shaped lake). From your comments I gather that I need the slope (angle), which I could take to be anything really. – KatyB Jan 10 '13 at 16:23