The bases of the trapezoid are 4 and 12, one of the sides is 12√3

The bases of the trapezoid are 4 and 12, one of the sides is 12√3, and the angle between it and one of the bases is 120. Find the area of the trapezoid

A trapezoid ABCD is given as in the figure. AB = 12, CD = 4, AB = 12 * root (3), angle BCD = 120.
Let us drop the height from point C to the base AB.
Angle BCE = Angle BCD – Angle ECD = 120 – 90 = 30 degrees.
Since the triangle CEB is rectangular, then
CE = BC * cos (BCE) = 12 * root (3) * root (3) / 2 = 18

Trapezium area:
S = ((AB + CD) / 2) * CE = (16/2) * 18 = 144

Answer: 144