The bisector of an obtuse angle of a parallelogram divides its side into 3 and 5 cm segments, counting

| February 8, 2021 | education

The bisector of an obtuse angle of a parallelogram divides its side into 3 and 5 cm segments, counting from the top of the acute angle. Calculate the area of a parallelogram if its acute angle is 60 degrees.

In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = (180 – 60) = 120.

ВK is the bisector of an obtuse angle, then the angle AВK = 120/2 = 60.

Then in the triangle ABK two acute angles are equal to 60, then the triangle ABK is equilateral, AB = BK = AK = 3 cm.

The height BH of an equilateral triangle is also the height of the parallelogram.

ВН = AK * √3 / 2 = 3 * √3 / 2 cm.

Parallelogram length AD = AK + DC = 3 + 5 = 8 cm.

Then Savsd = AD * ВН = 8 * 3 * √3 / 2 = 12 * √3 cm2.

Answer: The area of the parallelogram is 12 * √3 cm2.



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