a few math team problems need help with

1. from a point within an equilateral triangle, perpendiculars of length 3,6,9 are dropped to the sides. find the area of the triangle.

2. What is the distance between the incenter and circumcenter of a triangle with sides of the length 12, 16 and 20 (*sidenote* 3,4,5 triangle right there)

3. A right triangle's hypotenuse has projections of length 4 and 9. find the area of the triangle.

4. A 6ft. tall man is standing 3ft away from a 9ft tall light source. How long is his shadow

You don't have to answer all of them. answer the ones you can and provide a solution i will really appreciate it thank you!

-Amer