The bottom portion of the figure, quadrilateral BCGE , may be composed into a larger rectangle with base EG. The area of this composed rectangle is 24 square meters.
The triangles that need to be subtracted from the composed rectangle to find the area bounded by BCGE each have a base of 4 meters and a height of 6 meters.
The area of triangle BFC is 30 square meters.
The total area of the figure is 48 square meters.