The sides of the parallelogram are 7: 3, one of them is 12cm smaller than the other.
| September 5, 2021 | education
The sides of the parallelogram are 7: 3, one of them is 12cm smaller than the other. Find the area of a parallelogram if its angle is 120 degrees.
One side of a parallelogram is 7 parts, the other side of a parallelogram is 3 parts. Let’s find the difference of the sides in parts.
7 – 3 = 4 parts.
The difference in 4 parts is 12 centimeters. Let’s find the length of one part.
12 cm ÷ 4 = 3 cm.
Find the length of one side.
7 * 3 cm = 21 cm.
Find the length of the other side.
3 * 3 cm = 9 cm.
Find the area of the parallelogram. Multiply one side by the other and by the sine of the angle between them.
S = 21 cm * 9 cm * sin120 ° = 189 cm² * 0.866 = 163.67 cm².
Answer: the area of the parallelogram is 163.67 cm².
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