The perimeter of the rhombus is 20 cm, and one of its corners is 30 degrees. Find the height of the diamond.

The perimeter of the rhombus is 20 cm, all sides of the rhombus are equal, we calculate the length of the side of the rhombus:

20: 4 = 5 (cm) – rhombus side.

A rhombus is also a parallelogram, the formula for finding the area of a parallelogram is:

S = a * b * sina (a and b are adjacent sides of the parallelogram, a is the angle between them).

Let’s calculate the area of a rhombus: S = 5 * 5 * sin30 ° = 25 * 1/2 = 12.5 (cm²).

The area of a parallelogram can also be found using the formula:

S = a * h (a is the side of the parallelogram, h is the height drawn to this side).

The equation turns out: 12.5 = 5 * h.

5h = 12.5.

h = 12.5: 5 = 2.5 (cm).

Answer: The height of the rhombus is 2.5 cm.