Find the area of a rhombus if the angle C is 120 degrees, AC = 10.5.

univerkov | June 10, 2021 | education

The diagonals of the rhombus at the point of their intersection are halved and intersect at right angles. Then AO = OС = AC / 2 = 10.5 / 2 = 5.25 cm, OB = OD = BD / 2, and the ВOС triangle is rectangular.

The diagonals of the rhombus are the bisectors of the angles at their vertices, then the angle ВСО = 120/2 = 60.

In a right-angled triangle ВOС, tg60 = OB / OС.

ОВ = OС * tg60 = 5.25 * √3 cm.

Then ВD = 2 * ОВ = 10.5 * √3 cm.

Determine the area of the rhombus.

Savsd = АС * ВD / 2 = 10.5 * 10.5 * √3 / 2 = 441 * √3 / 8 cm2.

Answer: The area of the rhombus is 441 * √3 / 8 cm2.

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