Question:
What is the area, in square units, of an isosceles right triangle with a hypotenuse of 20 units?

Answer:
Each leg of a 45-45-90 triangle with a hypotenuse of 20 units measures $\frac{20}{\sqrt{2}}$ units.  The area is $\frac{1}{2}(\text{base})(\text{height})=\frac{1}{2}\left(\frac{20}{\sqrt{2}}\right)\left(\frac{20}{\sqrt{2}}\right)=\frac{400}{2\cdot 2}=\boxed{100\text{ square units}}$.