ABCD parallelogram AD = 12 cm, AB = 20 cm, angle B = 150 ° find the area ABCD.

The area of ​​a parallelogram is calculated as the product of one side by the height drawn to it. Let’s draw the height to the side AD – BH. Its value is not known by the statement of the problem.

But the angle B is given equal to 150. From it you can find the angle A: since the sum of adjacent angles in the parallelogram is 180, the angle A = 180 – 150 = 30.

Triangle ABH is rectangular. This means that the sine of angle A is equal to the ratio of the opposite leg to the hypotenuse, and that is:

sin (A) = BH / AB. Therefore BH = AB * sin (A) = 20 * (1/2) = 10.

It remains to substitute the found height into the formula for the parallelogram area: S (ABCD) = AD * BH = 12 * 10 = 120 cm2.