The perimeter of the parallelogram is 80 cm. Its sides are 2: 3, and the acute angle is 30 °.

The perimeter of the parallelogram is 80 cm. Its sides are 2: 3, and the acute angle is 30 °. Find the area of the parallelogram.

ABCD – parallelogram,

AB – BC = 5 centimeters,

the ABCD perimeter is 80 centimeters.

Find the area of ​​the parallelogram ABCD -?

Solution:

Consider a parallelogram ABCD. Its opposite sides are equal to each other, then BC = AD, AB = CD.

Let the length of the BC side be 2 * x centimeters, then the length of the AB side = 3 * x centimeters. We know that the ABCD perimeter is 80 centimeters. Let’s make the equation:

R avsd = AB + CD + BC + AD;

80 = 2 * x + 2 * x + 3 * x + 3 * x;

10 * x = 80;

x = 80: 10;

x = 8 centimeters;

2 * 8 = 16 centimeters – the lengths of the sides ВС and АD;

3 * 8 = 24 centimeters – lengths of sides AB and CD.

S = 16 * 24 * 1/2 = 192 cm ^ 2.

Answer: 192 cm ^ 2.