The heights of the parallelogram drawn from the apex of the obtuse angle indicate

univerkov | April 10, 2021 | education

The heights of the parallelogram drawn from the apex of the obtuse angle indicate an angle of 30 degrees. Find the area of the parallelogram if its sides are 16 cm and 20 cm.

Consider a quadrangle BPDH, in which the angles H and P are straight, then the angle PDH = 360 – 90 – 90 – 30 = 150.

Since the parallelogram has a sum of adjacent angles equal to 180, the angle BAD = 180 – 150 = 30.

Then, in a right-angled triangle ABН, the ВН leg lies opposite the angle 30, then ВН = AB / 2 = 16/2 = 8 cm.

Determine 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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