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 -?
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.
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