Pinwheel Area Problem

Here is another engaging problem from Presh Talwalkar.

___________Triangle Area 1984 AIME
Point P is in the interior of triangle ABC, and the lines through P are parallel to the sides of ABC. The three triangles shown in the diagram have areas of 4, 9, and 49. What is the area of triangle ABC?”

Answer.

See the Pinwheel Area Problem. for solutions.