In a parallelogram, one of the stars is 12 cm, and one of the angles is 150 degrees.

In a parallelogram, one of the stars is 12 cm, and one of the angles is 150 degrees. Find the area of the parallelogram if its perimeter is 48 cm.

Find the second side of the parallelogram, knowing its perimeter:
48/2 – 12 = 12 (cm).
Find the second corner of the parallelogram:
180 ° – 150 ° = 30 ° (angles adjacent to one side of the parallelogram).
Lower the height from the top of the parallelogram (150 °). We get a right-angled triangle, the acute angle of which is 30 °, the hypotenuse (side of the parallelogram) = 12 cm.
The unknown leg (height) is equal to half the hypotenuse, 6 cm.
We find the area of the parallelogram using the formula:
S = a * h = 12 * 6 = 72 (cm²).
Answer: the area is 72 cm².