In a parallelogram, the heights are 3 and 5, and the acute angle is 30 degrees. Find the area of the parallelogram.
| June 1, 2021 | education
Parallelogram area ABCD:
S = AD * BK, where AD is the parallelogram side, ВK is the height to the AD side; BK = 3;
DH – height to the AB side; DH = 5;
In triangle АDН HD – leg, lying opposite an angle of 30 °;
HD = 1/2 AD; AD = 2 * HD = 2 * 5 = 10;
S = 10 * 3 = 30;
S = AB * DH; AB = S: DH = 30: 5 = 6.
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