Hi!

Today found this task:

A pyramid has parallelogram at its bottom, the surface area of it is 360 cm^2, but the area of pyramids surface (without the parallelogram) is 768 cm^2. Edges or parallelogram is 20 and 36. Need to calculate the height of pyramid. Said also that the hight is where both parallelogram's diagonals cross. I only know the answer - 12 cm.

(E on top)

So the area of ABCD = 360 cm^2, Area of AEB + BEC + CED + DEA = 768 cm^2

AB = 20 cm, BC = 36 cm. EF is the height.

Sadly I didn't get far, found a way to get diagonals length (both) and found that it could be really easy if I somehow got EB, then I get 2 right triangles and easy to get the height. Can't figure out what to do with the surface area...

found that the area is 2 times area of both side triangles, but found a problem that I can't get the height of the triangle and there is no connection with the parallelogram.