# One of the angles of the parallelogram is 150 degrees and the diagonal is 6 perpendicular

**One of the angles of the parallelogram is 150 degrees and the diagonal is 6 perpendicular to the side, find the perimeter of the parallelogram.**

Since ABCD is a parallelogram, the sum of its adjacent angles is 180.

Then the angle BAD = 180 – ABC = 180 – 150 = 30.

By condition, the diagonal BD is perpendicular to the lateral side AB, then the triangle ABD is rectangular, in which the angle BAD = 30.

Leg BD of triangle ABD lies opposite angle 30, then BD = AD / 2.

AD = 2 * BD = 2 * 6 = 12 cm.

By the Pythagorean theorem, we determine the length of the leg AB.

AB ^ 2 = AD ^ 2 – BD ^ 2 = 144 – 36 = 108.

AB = 6 * √3 cm.

In a parallelogram, opposite sides are equal.

Determine the perimeter of the parallelogram.

P = 2 * (AB + AD) = 2 * (6 * √3 + 12) = 12 * (√3 + 2) cm.

Answer: The perimeter of the parallelogram is 12 * (√3 + 2) cm.