Perimeter of A Rhombus

Perimeter of a Rhombus is the sum of all the sides of the rhombus. In a rhombus, all the sides are equal so the perimeter of the rhombus is 4 times its side. The perimeter of Rhombus is calculated by the formula P = 4a where a is the side length of the perimeter. Now we can also find the perimeter of the rhombus with diagonals. This formula for the perimeter of the rhombus with the diagonals is added below in the article.

In this article we, will learn about What is Rhombus? Perimeter of Rhombus, Formula for Perimeter of Rhombus, and others in detail.

What is a Rhombus?

A rhombus is a parallelogram such that its four sides are equal to each other. Rhombus is an equilateral quadrilateral. The opposite sides of a rhombus are parallel to each other and its opposite angles are equal. The diagonals of a rhombus are perpendicular bisectors of each other. All the angles in a Rhombus may or may not be equal. The image representing the rhombus is added below,

The above figure depicts a rhombus ABCD with sides AB, BC, CD and AD of equal length and diagonals AC and BD divides each other into two equal parts.

What is Perimeter of Rhombus?

Perimeter of a Rhombus is the sum of all the sides of the Rhombus. In the figure added above we have a rhombus ABCD, then the perimeter of rhombus is,

Perimeter of Rhombus ABCD = (AB + BC + CD + DA) units

For a rhombus all the sides are equal so, AB = BC = CD = DA = a(let). So the formula for the perimeter of rhombus is,

Perimeter of Rhombus = 4a

Perimeter of a Rhombus Formula

Perimeter of a rhombus is equal to the sum of all its sides. Since all sides of a rhombus are equal to each other, its perimeter is defined as four times of its side lengths. For example, if one side of a rhombus measures x units, its perimeter is given by 4x units. Perimeter of Rhombus Formula is given in two forms

• Perimeter of Rhombus Formula with Sides
• Perimeter of Rhombus Formula with Diagonals

Perimeter of Rhombus Formula With Sides

The formula used for measuring the perimeter of Rhombus when its sides are given is,

P = 4a

where,

• P is Perimeter of Rhombus
• a is Side of Rhombus

Perimeter of Rhombus With Diagonals

If the diagonals of the rhombus are given them its perimeter is calculated by using Pythagoras Theorem. Suppose we are given a rhombus with diagonals of length p units and q units then perimeter of rhombus is calculated by the formula,

Perimeter of Rhombus = 2√(p² + q²)

How to Find Perimter of Rhombus?

Perimeter of a Rhombus is found by following the steps added below,

Step 1: Note all the given dimasions of the Rhombus (Sides OR Diagonals)

Step 2: Use the suitable perimeter of rhombus formula added above.

Step 3: Simplify the value in step 2 to get the required perimeter of the Rhombus.

Perimeter of Rhombus Examples

Example 1: Find the perimeter of a rhombus if its side length is 4 m.

Solution:

Given,

• a = 4

Perimeter of Rhombus(P) = 4a

P = 4 (4) = 16 m

Thus, the perimeter of rhombus is 16 m.

Example 2: Find the perimeter of a rhombus if its side length is 7 m.

Solution:

Given,

• a = 7

Perimeter of Rhombus(P) = 4a

P = 4 (7) = 28 m

Thus, the perimeter of rhombus is 28 m.

Example 3: Find the perimeter of a rhombus if its side length is 10 m.

Solution:

Given,

• a = 10

Perimeter of Rhombus(P) = 4a

P = 4 (10) = 40 m

Thus, the perimeter of rhombus is 40 m.

Example 4: Find the side length of a rhombus if its perimeter is 96 m.

Solution:

Perimeter of Rhombus(P) = 4a

Given,

• P = 96

a = P/4

a = 96/4 = 24 m

Thus, the side of rhombus is 24 m.

Example 5: Find the side length of a rhombus if its perimeter is 52 m.

Solution:

Perimeter of Rhombus(P) = 4a

Given,

• P = 52

a = P/4

a = 52/4 = 13 m

Thus, the side of rhombus is 13 m.

Example 6: Find the perimeter of Rhombus with diagonals 10 and 24.

Solution:

Given,

• First Diagonal of Rhombus(p) = 10 units
• Second Diagonal of Rhombus(q) = 24 units

Perimeter of Rhombus(P) = 2√(p² + q²)

P = 2√(10² + 24²) = 52 units

Thus, the perimeter of Rhombus is 52 units.

Practice Questions on Perimeter of Rhombus

Q1. Find the perimeter of rhombus if its sides is 12 m.

Q2. Find the perimeter of rhombus if its sides is 2 mm.

Q3. What is the side of rhombus whose perimeter is 24 cm?

Q4. What is the side of rhombus whose perimeter is 44 m?

FAQs on Perimeter of Rhombus

1. Define Rhombus

Rhombus is a 2-D figure in which all four sides are equal. It is a regular quadrilateral and is not same as square.

2. What is Formula of Perimeter of Rhombus?

Perimeter of Rjombus is the sum of all the sides of the rhombus. In rhombus all the sides are equal. So if the side of a rhombus is “a” units then the perimeter of Rhombus formula is,

Perimeter of Rhombus = 4a

3. What is Area of Rhombus?

Area of rhombus is the space occupied by the boundries of the rhombus. It is total area inside the perimeter of the rhombus.

4. What is Formula for Area of Rhombus?

The formula for finding the area of rhombus is,

Area of Rhombus = b × h

where,

• b is base of Rhombus
• h is height of Rhombus

5. What are Properties of Rhombus?

A rhombus is a quadrilateral and some of its important properties are,

• All the sides of a rhombus are equal.
• Diagonals of a rhombus are perpendicular bisector to each other.
• Opposite angles of a rhombus are equal, etc.

6. What is the Perimeter of a Rhombus with Diagonals?

The perimeter of rhombus if digonals are given is,

Perimeter = 2√(p² + q²)

where,

• p and q are its diagonals

7. What is the Perimeter of a Rhombus whose Diagonals are 16 and 30?

Perimeter of Rhombus whose digonals are 16 and 30 is,

P = 2√(16² + 30²) = 2√(256 + 900) = 2√(1156) = 34 units

8. What is the Perimeter of a Rhombus with Diagonals 10 and 24?

Perimeter of Rhombus whose digonals are 10 and 24 is,

P = 2√(10² + 24²) = 2√(100 + 576) = 2√(676) = 26 units