The diagonals of the rhombus are 12 cm and 16 cm. Find the area and perimeter of the rhombus.

The area of a rhombus is equal to half the product of its diagonals:

S = 1/2 * d1 * d2;

S = 1/2 * 12 * 16;

S = 6 * 16;

S = 96 cm².

To find the perimeter, let’s find the sides of the rhombus. The diagonals of the rhombus are mutually perpendicular and are halved by the point of intersection. Let’s find the sides of the rhombus according to the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse:

a² + b² = c²;

(1/2 d1) ² + (1/2 d2) ² = c²;

(1/2 * 12) ² + (1/2 * 16) ² = c²;

6² + 8² = c²;

36 + 64 = c²;

c² = 100;

c = √100;

c = 10 cm – rhombus side.

Find the perimeter by adding all the sides:

P = 10 + 10 + 10 + 10 = 40 cm.