Find the perimeter and area of the diagonal rhombus of which is 24 cm and 32 cm.

Let’s define the area of a rhombus through its diagonals.

Savsd = АС * ВD / 2 = 32 * 24/2 = 384 cm2.

The diagonals of the rhombus, at the intersection point, are divided in half and intersect at right angles, then AO = AC / 2 = 32/2 = 16 cm, OB = BD / 2 = 24/2 = 12 cm, and the AOB triangle is rectangular.

In a right-angled triangle AOB, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AO ^ 2 + BO ^ 2 = 256 + 144 = 400.

AB = 20 cm.

In a rhombus, the lengths of the sides are equal, then AB = BC = CD = AD = 20 cm.

The perimeter of the rum is: P = 4 * AB = 4 * 20 = 80 cm.

Answer: The area of the rhombus is 384 cm2, the perimeter of the rhombus is 80 cm.