The adjacent sides of the parallelogram are 32 cm and 26 cm, and one of its angles is 150 degrees

The adjacent sides of the parallelogram are 32 cm and 26 cm, and one of its angles is 150 degrees. Find the area of the parallelogram.

Let a parallelogram ABCD be given, in which the adjacent sides AD = 32 cm, AB = 26 cm, ∠ABС = 150 °. To find the area of the parallelogram, use the formula:
S = АD ∙ АВ ∙ sin ∠ВАD, where ∠ВАD = 180 ° – ∠ABS = 180 ° – 150 ° = 30 ° – by the property of one-sided angles of a parallelogram. Then S = 32 cm ∙ 26 cm ∙ sin 30 ° = 416 cm ^ 2.
Answer: The area of the parallelogram is 416 cm ^ 2.