Find the area of a parallelogram if its two sides are 6 cm and 8 cm, and one of the corners is 150 degrees.

The task requires to find the area of ​​a parallelogram along two sides and an obtuse angle between them. When calculating the area by the formula S = a * b * sin A, you can use the reduction formulas, or you can use the property “The sum of the angles of a parallelogram adjacent to one side is 180 °”. Draw a visual drawing and plot these tasks on the drawing.

Given: parallelogram, a = 6 cm, b = 8 cm, angle A is 150 °.

Find: S.

Decision:

Angles A and B are adjacent to side AB.
The sum of the angles A and B is 180 °.
180 ° – 150 ° = 30 ° angle B.
S = a * b * sin B.
S = 6 * 8 * sin 30 ° = 6 * 8 * 0.5 = 24 (sq. Cm).
Answer: The area of ​​the parallelogram is 24 square centimeters.