Introduction
A rhombus is a flat shape that has four equally sized sides and four potentially non-90° angles. A parallelogram is not always a rhombus, but a rhombus is always a parallelogram. Rhombuses are frequently referred to as diamonds or diamond-shaped objects. The perimeter of a rhombus is the entire distance traversed along its edge. Due to the fact that a square meets all the criteria for becoming a rhombus, we can also refer to a square as a rhombus.
The length of each side is added to determine the perimeter of a rhombus, which is the overall measurement of its boundary, as mentioned earlier. Since each of the four sides of a rhombus has an equal length, the perimeter of a rhombus may be calculated using the formula,
Perimeter = 4a, where ‘a’ denotes the length of the side of a rhombus. Inches, yards, millimeters, and other linear units are used to express the perimeter of a rhombus.
The Fundamental Characteristics of a Rhombus
- All the sides are congruent
- Opposite sides are parallel to each other
- Height is the shortest distance between the parallel sides
- Diagonals bisect each other at 90 degrees
Formula for the Perimeter of a Rhombus
Consider a rhombus with side length ‘a’. The perimeter is then 4a, which is equal to a + a + a + a.
As a result, P = 4a is the required formula.
Solved Examples
Example 1: Find the perimeter of a rhombus having a side length of 6 centimeters.
Solution:
Given that, side length ‘a’ = 6 centimeters.
Using the formula for the perimeter of a rhombus.
P = 4a
P = 4 \(\times\) 6
P = 24 centimeters.
Therefore, the perimeter of a rhombus having a side length of 6 centimeters is 24 centimeters.
Example 2: Find the perimeter of a rhombus having a side length of 12 inches.
Solution:
Given that, side length ‘a’ = 12 inches.
Using the basic formula of the perimeter of a rhombus.
P = 4a
P = 4 \(\times\) 12
P = 48 inches.
Therefore, the perimeter of a rhombus having a side length of 12 inches is 48 inches.
Example 3: Find the perimeter of a plot shaped like a rhombus and which has a side length of 43 feet.
Solution:
Given that, side length of the plot ‘a’ = 43 feet.
Using the basic formula of the perimeter of a rhombus.
P = 4a
P = 4 \(\times\) 43
P = 172 feet.
Therefore, the perimeter of the plot having a side length of 43 feet is 172 feet.
The perimeter of a rhombus is calculated by multiplying one of its four equal sides by four 4. Four times the length of one the sides is applied to determine the perimeter of a rhombus.
We are aware that the formula four times the side length can be used to get the perimeter of a rhombus with a specific side length. Thus, by dividing the perimeter by 4, we can obtain the side length.
A rhombus is a flat shape having four equally sized sides and four angles that are not right angles.
Yes, a rhombus is always a parallelogram.
No, a parallelogram is not always a rhombus.