The angle of the parallelogram is 150 (degrees), and the sides are 11 cm and 3√3 cm.

| September 6, 2021 | education

The angle of the parallelogram is 150 (degrees), and the sides are 11 cm and 3√3 cm. Find the S of the parallelogram and its smaller diagonal.

The area of a parallelogram is equal to the product of the sides of the parallelogram multiplied by the sine of the angle between them.

S = AB * AD * SinABC = 3 * √3 * 11 * Sin150 = 33 * √3 * 1/2 = 16.5 cm2.

The sum of the adjacent angles of the parallelogram is 180, then the angle BAD = 180 – 150 = 30.

From the triangle ABD, by the cosine theorem, we determine the length of the diagonal BD.

BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * CosBAD = (3 * √3) 2 + 112 – 2 * 3 * √3 * 11 * Cos30 = 27 + 121 – 66 * √3 * √3 / 2 = 148 – 99 = 49.

ВD = √49 = 7 cm.

Answer: The area of the parallelogram is 16.5 cm2, the smaller diagonal is 7 cm.



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