Triangle in a Quadrilateral

Given the ratio of a quadrilateral’s length to width, find the ratio of the area of a special shaded region to the area of the quadrilateral.


“Quadrilateral ABCD is a rectangle with length to width in the ratio of 3 : 2. AN and BM are bisectors of angle A and angle B, respectively. What is the ratio of the area of the shaded region to the area of ABCD? Explain your solution.

Extension:
How does your answer change if quadrilateral ABCD is a parallelogram?