The adjacent sides of the parallelogram are 52 cm and 30 cm, and the acute angle is 30 degrees.

The adjacent sides of the parallelogram are 52 cm and 30 cm, and the acute angle is 30 degrees. Find the area of the parallelogram.

A parallelogram is a quadrilateral in which the opposite sides are pairwise parallel and equal to each other:

AB = CD;

BC = AD.

In order to calculate the area of a parallelogram, we use the area formula through the sides and the sine of the angle between them:

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

S is the area of the parallelogram;

a, b – sides of the parallelogram;

α, ß – angles of the parallelogram.

sin 30º = 1/2;

S = 52 ∙ 30 ∙ 1/2 = 1560/2 = 780 cm2.

Answer: the area of the parallelogram is 780 cm2.