The heights of the parallelogram drawn from the apex of the obtuse angle form an angle of 30 °.

| May 29, 2021 | education

The heights of the parallelogram drawn from the apex of the obtuse angle form an angle of 30 °. find the area of the parallelogram if its sides are 16 cm and 20 cm.

Consider a quadrangle КBНD, which, according to the condition, has an angle КBН = 30, and the angles BКD and ВНD are straight, since ВК and ВН are the heights of the parallelogram.

Then the angle КDН = АDС = 360 – 30 – 90 – 90 = 150.

Since the parallelogram has opposite angles, the angle ABC = ADC = 150.

The sum of the adjacent angles of the parallelogram is 180, then the angle BAD = 180 – ABC = 180 – 150 = 30.

Then, in a right-angled triangle AKB, the leg BK is erect against an angle of 30, and therefore is equal to half the length of the hypotenuse AB. BK = AB / 2 = 16/2 = 8 cm.

Determine the area of ​​the parallelogram.

Savsd = AD * BK = 20 * 8 = 160 cm2.

Answer: The area of ​​the parallelogram is 160 cm2.



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