In a parallelogram ABCD, AB = 13 AD = 5, and the angle B is 150 degrees. Find the area of the parallelogram.

In the parallelogram we find the angle A, it is adjacent to the angle B, which is 150 ° by condition.
Angle A = 180 ° – 150 ° = 30 °.
From the vertex B, let us lower the height BH to the AD side. In a right-angled triangle, VN is a leg that lies opposite an angle of 30 °. By the property of the leg, it is equal to half the hypotenuse:
BH = 1/2 * AB = 1/2 * 13 = 6.5.
Find the area of the parallelogram as the product of the side and the height drawn to it.
S = a * h = AD * BH = 5 * 6.5 = 32.5
It was possible to find the area through the sides and the angle between them:
S = a * b * sin a = AB * AD * sin 30 ° = 13 * 5 * 1/2 = 32.5
Answer: the area is 32.5.