Trapezoid ABCD, M is the waist midpoint of AD, triangle ABM area is 8, triangle MCD is 12, calculate the area of triangle BMC

Trapezoid ABCD, M is the waist midpoint of AD, triangle ABM area is 8, triangle MCD is 12, calculate the area of triangle BMC

ABM and MCD are equal in height, so AB / DC = 8 / 12 = 2 / 3, so AB = 2 / 3DC
ABCD=(AB+DC)AD/2=5/6DC*AD=5/3*DC*DM
And DC * DM / 2 = 12
So ABCD = 5 / 3 * 12 * 2 = 40
BCM=40-8-12=20