Find the area of a parallelogram with sides of 3 cm and 5 cm and an angle of 150 degrees.

univerkov | August 1, 2021 | education

1. Vertices of the parallelogram A, B, C, D. ∠B = 150 °. BH – height (drawn to the side of blood pressure). AB = 3 centimeters. AD = 5 centimeters. S – area.

2. ∠АВН = 150 ° – ∠СВН = 150 ° – 90 ° = 60 °.

3. We calculate the length of BH in terms of one of the trigonometric functions ∠АВН (cosine):

BH: AB = cosine 60 ° = 1/2.

BH = 1 / 2AB = 3/2 = 1.5 centimeters.

4. S = AD x BH = 5 x 1.5 = 7.5 centimeters².

Answer: S equals 7.5 centimeters².

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