In a parallelogram, an obtuse angle is 150 degrees. The bisector of this angle divides the side of the parallelogram

| September 24, 2021 | education

In a parallelogram, an obtuse angle is 150 degrees. The bisector of this angle divides the side of the parallelogram into 16 cm and 5 cm segments, counting from the top of the acute angle. Find the area of the parallelogram.

Since DK, by condition, is the bisector of the ADC angle, it cuts off the equilateral triangle DCK, in which CD = CK = 16 cm.

Let’s draw the height DH to the BC side.

The sum of the adjacent angles of the parallelogram is 180, then the angle DСВ = (180 – ADС) = (180 – 150) = 30. Then in the right-angled triangle СDН the leg DН lies opposite the angle 30, then DН = СD / 2 = 16/2 = 8 cm .

Side BC = BK + CK = 5 + 16 = 21 cm.

Determine the area of the parallelogram.

Savsd = BC * DH = 21 * 8 = 168 cm2.

Answer: The area of the parallelogram is 168 cm2.



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