See the following image ( not to scale)
Call the length of the longer base, AB = P and the length of the shorter base, GF = Q
Then AF = Q + ( P - Q) / 2 = (P + Q) / 2 = the median length = M
So....since the median = the height, we have right triangle AFD such that
AF^2 + FD^2 = AD^2 where AF, FD = M and AD = 12
M^2 + M^2 = 12^2
2M^2 = 144
M^2 = 72
M = 6sqrt (2) = height
So....the area = (1/2) height * (sum of the bases) = height * (sum of bases)/2 =
height * median =
(6sqrt (2) ) ( 6sqrt (2)) = 36 * 2 = 72 units^2