The bottom portion of the figure, quadrilateral ABCD, may be composed into a larger rectangle with base 4 meters. The area of this composed rectangle is 40 square meters.
The triangles that need to be subtracted from the composed rectangle to find the area bounded by ABCDE each have a base of 2 meters and a height of 4 meters.
The area of triangle ABE is 4 square meters.
The total area of the figure is 40 - 2(4) = 32 square meters.