The height of the parallelogram is 8 cm, 4 cm, the angle between them = 30. Find the area of the parallelogram.
| April 27, 2021 | education
In the quadrangle BKDН, we determine the value of the НDK angle.
Angle НDК = АDС = 360 – ВНD – НВК – ВКD = 360 – 90 – 30 – 90 = 150.
The sum of the adjacent angles of the parallelogram is 180, then the angle BAD = 180 – ADC = 180 – 150 = 30.
In a right-angled triangle ABН, the leg BH = 4 cm and lies against the angle 30, then AB = 2 * BH = 2 * 4 = 8 cm.
In a parallelogram, the lengths of the opposite sides are equal, then CD = AB = 8 cm.
Determine the area of the parallelogram.
Savsd = CD * BK = 8 * 8 = 64 cm2.
Answer: The area of the parallelogram is 64 cm2.
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