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The perimeter of a rhombus is the sum of all its sides. Rhombus is a quadrilateral in which all four sides are of the same measure. A rhombus is always a parallelogram but a parallelogram may not necessarily be a rhombus always. Let us study more about the perimeter of rhombus in this article.
Perimeter of Rhombus Formula
Perimeter refers to the total distance around the boundary or outer edge of a two-dimensional shape. It is the sum of all the lengths of the sides or segments that form the shape’s boundary. The perimeter of a rhombus is the total distance around its boundary.
The formula to calculate the perimeter of a rhombus depends on the given information about the rhombus. Here are a few scenarios:
- When the side length (s) is given: In a rhombus, all four sides are equal in length. Therefore, to find the perimeter, you can multiply the side length by 4:
Perimeter = 4 x s
- When the length of one diagonal (d1) is given: In a rhombus, the length of one diagonal is related to the side length by the following relationship: d1 = 2 x s. To find the perimeter, you can use this relationship and multiply the side length by 4:
Perimeter = 4 x (d1 / 2) = 2 x d1
- When the lengths of both diagonals (d1 and d2) are given: The perimeter can be found by adding the lengths of all four sides. Since the diagonals of a rhombus bisect each other at right angles, we can apply the Pythagorean theorem to relate the side length (s) and the diagonals:
s = √((d1/2)^2 + (d2/2)^2) Once the side length is determined, the perimeter can be calculated: Perimeter = 4 x s
These formulas provide different ways to calculate the perimeter of a rhombus depending on the given information.
Solved Examples of Perimeter of Rhombus Formula:
Example 1: The length of one side of a rhombus is 6 centimeters. What is the perimeter of the rhombus?
Solution: Given: Side length (s) = 6 cm
To find: Perimeter (P)
Using the formula for the perimeter of a rhombus: P = 4s
Substituting the given value: P = 4 x 6 P = 24 cm
Therefore, the perimeter of the rhombus is 24 centimeters.
Example 2: A rhombus has a perimeter of 32 meters. If all four sides are equal, what is the length of each side?
Solution: Given: Perimeter (P) = 32 m
To find: Side length (s)
Using the formula for the perimeter of a rhombus: P = 4s
Substituting the given value: 32 = 4s
Dividing both sides by 4: 8 = s
Therefore, each side of the rhombus has a length of 8 meters.
Example 3: A garden in the shape of a rhombus has a perimeter of 72 meters. The length of one diagonal is 20 meters. Find the length of each side of the rhombus.
Solution: Given: Perimeter (P) = 72 m Length of one diagonal (d1) = 20 m
To find: Length of each side (s)
We know that in a rhombus, the diagonals bisect each other at right angles, and the side length is related to the diagonals by the Pythagorean theorem.
Let’s denote the length of the other diagonal as d2.
Using the formula for the perimeter of a rhombus: P = 4s
Substituting the given value: 72 = 4s
Dividing both sides by 4: 18 = s
Therefore, each side of the rhombus has a length of 18 meters.
Now, we can find the length of the other diagonal using the relationship between the diagonals and the side length.
Using the Pythagorean theorem: s2 = (d1/2)2 + (d2/2)2
Substituting the known values: 18^2 = (20/2)2 + (d2/2)2
324 = 100 + (d2/2)2
(d2/2)2 = 324 – 100
(d2/2)2 = 224
d2/2 = √224
d2 = 2 x √224
d2 ≈ 29.8 meters
Therefore, the length of the other diagonal is approximately 29.8 meters.
Frequently Asked Questions on Perimeter of Rhombus Formula:
1: What is the formula for solving for a perimeter of a rhombus?
Answer: The formula for finding the perimeter (P) of a rhombus is: P = 4 x side length
In this formula, the side length refers to the length of any one side of the rhombus. By multiplying the side length by 4, you can determine the total distance around the boundary of the rhombus, which gives you its perimeter.
2: What is the formula of perimeter of rhombus if diagonals are given?
Answer: If the diagonals of a rhombus are given, the formula for finding the perimeter (P) is:
P = 2 √(d12 + d22)
In this formula, d1 and d2 represent the lengths of the diagonals of the rhombus. By squaring each diagonal, summing the squared values, taking the square root of the sum, and multiplying it by 2, you can calculate the perimeter of the rhombus. It’s important to note that the diagonals of a rhombus bisect each other at right angles, forming four right triangles within the rhombus. The formula utilizes the Pythagorean theorem to account for the relationship between the diagonals and the perimeter of the rhombus.
3: What is the property of rhombus perimeter?
Answer: The property of a rhombus perimeter is that it is equal to four times the length of any of its sides. In other words, the perimeter of a rhombus is the sum of all its side lengths.
Mathematically, if ‘s’ represents the length of a side of the rhombus, then the formula for the perimeter (P) can be stated as:
P = 4s
This property holds true for all rhombuses, regardless of the size or orientation of the shape.
4: Is every rhombus a kite?
Answer: Yes, every rhombus is a type of kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. A rhombus is a specific type of kite where all four sides are of equal length. Therefore, a rhombus can be considered as a special case of a kite.
However, it’s important to note that not all kites are rhombuses. In a general kite, the adjacent sides can have different lengths, while in a rhombus, all sides are equal. So, while every rhombus is a kite, not every kite is a rhombus.
5: How can you determine the side length of a rhombus if you know its perimeter?
Answer: If you know the perimeter (P) of a rhombus and want to determine the side length (s), you can use the formula:
s = P / 4
In this formula, dividing the perimeter by 4 will give you the length of each side of the rhombus. This formula works because a rhombus has four equal sides, so dividing the perimeter equally among the four sides gives you the length of each side.
6: What is the formula for the perimeter of a diamond?
Answer: The two diagonals of a diamond are halved at 90 degrees. The formula for the circumference of a diamond is very easy to calculate. That is, the circumference or P = 4 × a. Where “a” is the length of one side of the diamond.
7: What is the rhombus properties formula?
Answer: The formulae for rhombuses are defined for two attributes:
Area of a rhombus, A = 1/2 × d1 × d2, where d1 and d2 are diagonals of a rhombus.
The perimeter of a rhombus, P = 4 × a, where a is the side.
8: Is every square a rhombus?
Answer: Every square is a rhombus, but every rhombus is not a square.
