Calculate the area of the triangle using vectors

Attachment 26975 A triangular shade cloth is to be suspended by three poles of different heights as shown. The feet of the poles are 10 m from each other. The heights of the poles are in the diagram. Calculate the area of cloth needed.

The answer is supposed to be 43.5 m^2. Please help!!!

Use Pythagoras to evaluate the length of each side of the triangle, then apply Heron's Formula.