The perimeter of the rhombus is 20 cm, and one of its corners is 30 degrees. Find the height of the diamond.
April 30, 2021 | education
| 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.
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