In a parallelogram, 2 sides are 12 and 8 cm, respectively, and one of the angles is 150 degrees.

univerkov | July 13, 2021 | education

In a parallelogram, 2 sides are 12 and 8 cm, respectively, and one of the angles is 150 degrees. Find the area of the parallelogram.

1. The tops of the parallelogram – A, B, C, D. BK – height (drawn to the side AB. ∠B = 150 °.

The sides AB and AD are respectively 8 cm and 12 cm.

2. ∠АВК = 150 ° – 90 ° = 60 °.

3. The length of the height BK is calculated through one of the trigonometric functions ∠ABK (cosine):

BK / AB = cosine ∠ABK = cosine 60 ° = 1/2.

BK = AB x 1/2 = 8 x 1/2 = 4 cm.

4. Calculate the area S of the parallelogram:

S = AD x BK = 12 x 8 = 96 cm².

Answer: S is equal to 96 cm².

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