The diagonals of the rhombus are 10 and 12 cm. Find its area and perimeter.

The area of a rhombus can be defined as half the product of the diagonals:

S = 0.5 * d1 * d2 = 0.5 * 10 * 12 = 60 cm2.

Consider a right-angled triangle in which half of the diagonals of the rhombus are legs, the side of the rhombus is the hypotenuse. By the Pythagorean theorem:

a ^ 2 = (d1 / 2) ^ 2 + (d2 / 2) ^ 2 = (10/2) ^ 2 + (12/2) ^ 2 = 5 ^ 2 + 6 ^ 2 = 25 + 36 = 61;

The side of the rhombus is a = √61 ≈ 7.81 cm.

The perimeter of a rhombus is equal to the sum of the lengths of its sides: P = 4 * a = 4√61 ≈ 31.24 cm.