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

univerkov | July 13, 2021 | education

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

Given: ABCD – parallelogram; AB: BC = 2: 3; parallelogram perimeter ABCD = 80 cm, Angle BAD = 30 degrees.
Find S of parallelogram ABCD -?
Decision:
Let AB = 2x cm and side BC = 3x. Then the perimeter of the parallelogram ABCD = AB + BC + CD + DA and AB = DA, BC = CD, so the perimeter of the parallelogram ABCD = 2x + 2x + 3x + 3x; 80 = 2x + 2x + 3x + 3x; 80 = 10x; x = 80: 10; x = 8 cm. Therefore AB = DA = 2 * 8 = 16 cm; BC = CD = 3 * 8 = 24 cm. S parallelogram ABCD = 16 * 24 sin 30 degrees = 16 * 24 * 1/2 = 192 centimeters square.
Answer: 192 cm squared.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.