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Perimeter of Rhombus: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Perimeter of RhombusPerimeter of Rhombus: Definition and ExampleTable of ContentsPerimeter of a Rhombus Definition of Perimeter of a Rhombus

The perimeter of a rhombus is the total length of its outer boundary, measured in linear units such as feet, inches, or yards. A rhombus is a special quadrilateral (four-sided polygon) where all sides have equal length. It also has several important properties: opposite angles are congruent, adjacent angles are supplementary, opposite sides are parallel, and its diagonals bisect each other at right angles.

There are multiple ways to calculate a rhombus's perimeter depending on what information you have. If you know the side length, you can simply multiply it by 444. If you know the lengths of both diagonals, you can use a formula based on the Pythagorean theorem. You can even find the perimeter when given just one diagonal and one interior angle by using trigonometric relationships.

Examples of Finding the Perimeter of a Rhombus Example 1: Finding the Perimeter with Side Length Problem:

Find the perimeter of a rhombus with a side length of 888 inches.

Rhombus

Step-by-step solution:

Step 1, Recall the formula for the perimeter of a rhombus using side length. Since all sides of a rhombus are equal, we multiply the side length by 444.

Perimeter=4×Side Length\text{Perimeter} = 4 \times \text{Side Length}Perimeter=4×Side Length

Step 2, Substitute the known value into the formula.

Perimeter=4×8 inches\text{Perimeter} = 4 \times 8 \text{ inches}Perimeter=4×8 inches

Step 3, Calculate the final answer.

Perimeter=32 inches\text{Perimeter} = 32 \text{ inches}Perimeter=32 inches Example 2: Finding the Perimeter Using Diagonals Problem:

If the diagonals of the rhombus are 666 and 888 inches, then what is the perimeter of the rhombus?

Perimeter of a Rhombus

Step-by-step solution:

Step 1, Recall the formula for finding the perimeter of a rhombus when we know the diagonals.

Perimeter=2p2+q2\text{Perimeter} = 2\sqrt{p^2 + q^2}Perimeter=2p2+q2​ where ppp and qqq are the lengths of the diagonals.

Step 2, Substitute the given values into the formula.

p=6 inchesp = 6 \text{ inches}p=6 inches q=8 inchesq = 8 \text{ inches}q=8 inches Perimeter=262+82\text{Perimeter} = 2\sqrt{6^2 + 8^2}Perimeter=262+82​

Step 3, Calculate the values inside the square root.

62=366^2 = 3662=36 82=648^2 = 6482=64 36+64=10036 + 64 = 10036+64=100

Step 4, Find the square root and complete the calculation.

Perimeter=2100\text{Perimeter} = 2\sqrt{100}Perimeter=2100​ Perimeter=2×10\text{Perimeter} = 2 \times 10Perimeter=2×10 Perimeter=20 inches\text{Perimeter} = 20 \text{ inches}Perimeter=20 inches Example 3: Finding the Side Length from Perimeter Problem:

Find the side of a rhombus if the perimeter is 363636 feet.

Perimeter of a Rhombus

Step-by-step solution:

Step 1, Write down the formula for the perimeter of a rhombus in terms of its side length.

Perimeter=4×side\text{Perimeter} = 4 \times \text{side}Perimeter=4×side

Step 2, Set up an equation using the given perimeter value.

36 feet=4×side36 \text{ feet} = 4 \times \text{side}36 feet=4×side

Step 3, Solve for the side length by dividing both sides by 444.

side=364 feet\text{side} = \frac{36}{4} \text{ feet}side=436​ feet side=9 feet\text{side} = 9 \text{ feet}side=9 feet Comments(7)EEnglishTutorFaithNovember 6, 2025This glossary page on the perimeter of a rhombus is great! It's helped my students grasp the concept easily. Thanks for the clear examples!

BBassistSamNovember 4, 2025I've been looking for a clear def of rhombus perimeter for my students. This page is great! The examples really helped them grasp it.

MCMs. CarterSeptember 17, 2025This page was super helpful for explaining the perimeter of a rhombus to my kids! The examples made it easy for them to understand, and we even tried measuring a kite at home to practice. Thanks!

MCMs. CarterSeptember 10, 2025I used the perimeter of rhombus examples from this page to help my son with his geometry homework—it really made the concept click for him! The step-by-step explanation was super helpful.

MCMs. CarterAugust 27, 2025I used the Perimeter of Rhombus page to help my kid with their geometry homework—it’s so clear and easy to follow! The examples really made a difference. Thanks for the step-by-step explanation!

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