From the vertex of the angle of the rhombus, which is 120 degrees, a diagonal 6 cm long is drawn.

| March 15, 2021 | education

From the vertex of the angle of the rhombus, which is 120 degrees, a diagonal 6 cm long is drawn. Find the area of the rhombus.

The diagonals of the rhombus intersect at right angles, are halved at the point of their intersection, and are the bisectors of the angles.

Consider a right-angled triangle AOB, in which the angle AOB = 90, the angle ABO = ABC / 2 = 120/2 = 60, then the angle ВAO is 180 – 90 – 60 = 30.

The leg BO of the triangle lies opposite angle 30, then its length is equal to half the length of the hypotenuse AB. BO = BD / 2 = 6/2 = 3 cm.

AB = 2 * ВO = 2 * 3 = 6 cm.

In a rhombus, all sides are equal. AB = BC = CD = AD = 6 cm.

Then the perimeter of the rhombus is: P = 4 * AB = 4 * 6 = 24 cm.

Answer: The perimeter of the rhombus is 24 cm.



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