10. [6] Let $T$ be a right triangle with sides having lengths 3,4 , and 5. A point $P$ is called awesome if $P$ is the center of a parallelogram whose vertices all lie on the boundary of $T$. What is the area of the set of awesome points?
Answer:
$3 / 2$
Solution: The set of awesome points is the medial triangle, which has area $6 / 4=3 / 2$.