One of the angles of the parallelogram is 150 °. The adjacent sides are 10 cm. Find P and S of the parallelogram.

Let’s denote the parallelogram by ABCD. the adjacent sides of the parallelogram are equal, so this is a rhombus.

AB = BC = CD = AD;

1. Find the perimeter S = 4 * AB = 4 * 10 = 40.

2. The area of a rhombus is determined by the formula S = a * h, where a is the length of the side, h is the height of the rhombus. omit the height from point B. We denote BM. Triangle ABM is rectangular.

a = AB = BC = CD = AD = 10 cm;

From the property of a parallelogram, according to which the sum of adjacent angles in a parallelogram is 180 °, we find the value of the angle BAD. 180 ° – 150 ° = 30 °.

Find the height value:

h = BM = sin BAD * AB = 10/2 = 5;

S = 10 * 5 = 50 cm. Sq.