The parallelogram angle is 150 degrees and the sides are 11 cm and 3√3. Find the area of the parallelogram
| February 13, 2021 | education
The parallelogram angle is 150 degrees and the sides are 11 cm and 3√3. Find the area of the parallelogram and its smaller diagonal.
In a parallelogram, the sum of adjacent angles is 180, then the angle ВAD = 180 – ABC = 180 – 150 = 30.
Determine the area of the parallelogram.
Savs = AВ * AD * SinВСD = 3 * √3 * 11 * Sin30 = 33 * √3 / 2 = 16.5 * √3 cm2.
We define the VD diagonal by the cosine theorem.
ВD^2 = AВ^2 + AD^2 – 2 * AВ * AD * CosAВD = 27 + 121 – 2 * 3 * √3 * 11 * √3 / 2 = 148 – 99 = 49
ВD = 7 cm.
Answer: The area of the parallelogram is 16.5 * √3 cm2, the ВD diagonal is 7 cm.
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