Sacred Haven of Debauchery

We have a right triangle. Its hypotenuse is 12, and the altitude to the hypotenuse is 7. What is its area?

36
Side PUT = hypotenuse divided by the square root of 2, area = half the product of the sides. The height is not needed.

Even simpler - mentally complete it to a square with a side of 12 (the hypotenuse of the small triangle), the area is 144, and divide it into 4 parts.