The sides of the parallelogram are 4 and 7 cm and the angle between them is 150 degrees.

The sides of the parallelogram are 4 and 7 cm and the angle between them is 150 degrees. Find the area of the parallelogram.

1. A, B, C, D – the tops of the parallelogram. AB = 4 centimeters. BC = 7 centimeters. ∠В = 150 °.

2. From the vertex B we lower the perpendicular BH to the AD side.

3.∠АВН = 150 ° – 90 ° = 60 °.

4. We calculate the length of the leg BH of the right-angled triangle ABH through the cosine ∠ABH:

BH: AB = cosine ∠ABH = cosine 60 ° = 1/2.

BH = AB x 1/2 = 4 x 1/2 = 2 centimeters.

5. The area of the parallelogram is equal to ВС х ВН = 7 х 2 = 14 centimeters²

Answer: The area of the parallelogram is 14 centimeters².