Find the area of a rhombus whose perimeter is 120 cm, and one of the diagonals is 36 cm.

In a rhombus, the lengths of all sides are equal.

Then AB = BC = CD = AD = Ravsd / 2 = 120/4 = 30 cm.

The diagonals of the rhombus, at the intersection point, are divided in half and intersect at right angles, then AO = CO = AC / 2 = 36/2 = 18 cm, and triangle AOB is rectangular.

By the Pythagorean theorem, in the right-angled triangle AOB, we determine the length of the leg OB.

OB ^ 2 = AB ^ 2 – AO ^ 2 = 900 – 324 = 576.

OB = 24 cm.

Then BD = 2 * 24 = 48 cm.

Determine the area of the rhombus.

Savsd = АС * ВD / 2 = 36 * 48/2 = 864 cm2.

Answer: The area of the rhombus is 864 cm2.