The parallelogram heights, drawn from the top of the acute angle, form an angle of 150 degrees.
| February 11, 2021 | education
The parallelogram heights, drawn from the top of the acute angle, form an angle of 150 degrees. Find the area of the parallelogram if its sides are 12 cm and 18 cm.
Consider a quadrangle AРСK, in which, by condition, the angle PAK = 1500, and the angles AKС and AРС are straight, since AР and AK are parallelogram heights.
Then the angle РСК = ВСD = 360 – 150 – 90 – 90 = 30.
From the vertex D we draw the height of the DН, which in the right-angled triangle of the DНС lies opposite the angle 30, and therefore is equal to half the hypotenuse of the СD. DН = СD / 2 = 12/2 = 6 cm.
Determine the area of the parallelogram.
Savsd = BC * DН = 18 * 6 = 108 cm2.
Answer: The area of the parallelogram is 108 cm2.
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