The parallelogram has two sides 12 and 16 cm, and one of the angles is 150 degrees.

The parallelogram has two sides 12 and 16 cm, and one of the angles is 150 degrees. Find the area of the parallelogram.

A parallelogram is a quadrilateral with opposite sides parallel in pairs.

In order to calculate the area of a parallelogram, we use the area formula in terms of the sides and angles of a parallelogram:

S = a ∙ b ∙ sin α = a ∙ b ∙ sin ß, where:

a, b – sides of a parallelogram;

sin α, sin ß are the angles between them.

The sum of adjacent (adjacent) angles of a parallelogram is 180º. The sines of adjacent angles are equal, therefore:

sin α = sin ß;

sin 150 ° = sin (180º – 150º) = sin 30º = 1/2 = 0.5;

S = 12 ∙ 16 0.5 = 96 cm2.

Answer: the area of the parallelogram is 96 cm2.