In the parallelogram, one of the angles is 150 (degrees), and one of the sides is 10 cm.Find S if P = 56 cm.

ABCD – parallelogram
Let BC = AD = a = 10 cm
AB = CD = b
BH = h – parallelogram height
angle BAD = angle alpha = 150 degrees
P = 56 cm

Rparallel. = 2 * (a + b), where a and b are the sides of the parallelogram
Substitute the known values and get:
56 = 2 * (10 + b)
56 = 20 + 2b
56 – 20 = 2b
36 = 2b
36: 2 = b
18 = b

Consider a triangle ABH, the angle BHA is a straight line, because the height of the parallelogram falls perpendicularly. So triangle ABH is right-angled
sin alpha = h / b
sin = 0.5
0.5 = h / 18
h = 18 * 0.5
h = 9

Sparallel. = a * h
Sparallel. = 10 * 9
Sparallel. = 90
90 cm ^ 2 – parallelogram area

Answer: 90 cm ^ 2