In trapezoid ABCD with bases AD and BC, the angle B is equal to 150 degrees.

In trapezoid ABCD with bases AD and BC, the angle B is equal to 150 degrees. Find the area of the trapezoid if AB = 12 cm, AD = 15 cm, BC = 7 cm.

Let’s build the height BH of the trapezoid ABCD.

In a right-angled triangle ABN, we determine the values of acute angles.

Angle ABH = ABC – СBH = 150 – 90 = 60, then angle BAH = (180 – ABH – AHB) = (180 – 60 – 90) = 30.

The leg BH is located opposite the angle 30, then its length will be equal to half the length of the hypotenuse AB.

BH = AB / 2 = 12/2 = 6 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (7 + 15) * 6/2 = 66 cm2.

Answer: The area of the trapezoid is 66 cm2.