The hypotenuse of an isosceles right triangle is $4\sqrt{2}$ units. How many square units are in the area of the triangle?
The hypotenuse of an isosceles right triangle is $\sqrt{2}$ times the length of each leg, so each leg of the triangle has length 4.  Therefore, the area of the triangle is $(4)(4)/2 = \boxed{8}$ square units.