ABCD parallelogram AD 12cm, AB 20cm B 150 degrees. Find the area of a parallelogram.

It is known:

ABCD parallelogram;
AD = 12 cm;
AB = 20 cm;
Angle B = 150 °.
Find the area of the parallelogram.

1) BK – the height drawn from K to the AD side.

2) Triangle ABK – rectangular.

Angle K = 90 °;

Angle A = 30 °;

Find the leg BK of the ABK triangle.

sin A = BK / AB;

BK = AB * sin A;

Substitute the known values and calculate the BK.

BK = AB * sin 30 ° = 20 * 1/2 = 20/2 = 10;

3) The height of the parallelogram is BK = 10.

4) Find the area of the parallelogram. The area is equal to the product of the height and the base.

S = AD * BK = 12 * 10 = 120 cm ^ 2.