The heights of the parallelogram, drawn from the top of the obtuse angle, form an angle of 30
| July 2, 2021 | education
The heights of the parallelogram, drawn from the top of the obtuse angle, form an angle of 30 degrees. Find the area of the parallelogram if its sides are 16cm and 20cm.
In the quadrangle BKDN, we define the value of the angle KDH = ADC.
Angle КDН = 360 – 90 – 90 – 30 = 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 ABH, the BH leg lies opposite an angle of 30, then BH = AB / 2 = 16/2 = 8 cm.
Let’s clean up the area of the parallelogram.
Savsd = AD * BH = 20 * 8 = 160 cm2.
Answer: The area of the parallelogram is 160 cm2.
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