The area of the lower region is 1/2*54*d

The area of the upper region is 1/2*30*e

Since those areas are equal we know that e/d = 54/30 = 9/5

Since the triangles with hypotenuse a and 13 are similar we know that a/13 is also 9/5.

a is therefore 23.4.

If the lower area is x, then the total area below the dashed line is 9x/5.

Since the total area must be 3x, the area above the dashed line must be 6x/5. It follows from this that b/30 must be 6/5.

b is therefore 36.

Since 54 = 36 + 2c, c=9.

To find e we use Pythagoras on the ace triangle. e = 21.6.

The total area of the trapezoid is therefore 21.6*(54+36)/2 = 972