# Rhombus

"What is a rhombus?" asked Miss Granger in geometry class.

Nicole, who had always loved geometry said, "A rhombus is also a parallelogram, but because of its unique properties, it gets an individual identity as a quadrilateral."

When you ask someone the question: 'What is a rhombus?,' then Nicole's answer is almost perfect.

In this section, we’re going to look at the rhombus definition, understand the rhombus shape, learn about the area of a rhombus, as well as its perimeter. But before we get into those details, let's also look at properties of a rhombus, and its unique diamond geometric shape. ## Lesson Plan

 1 What is a Rhombus? 2 Important Notes on Rhombus 3 Solved Examples on Rhombus 4 Interactive Questions on Rhombus 5 Tips and Tricks

## What is a Rhombus?

The rhombus is an interesting quadrilateral because of its unique shape.

While all its sides are equal, it is not a square because all its angles are $$90^\circ$$.

In this chapter, we will explain the properties of a rhombus and why it's quite a cool quadrilateral.  Like most things in math, the name "rhombus" comes from Ancient Greece from the word "rhombos," which means a piece of wood whirled on a string to make a roaring noise. Today, however, we see rhombus-shaped figures every day. Look at the diamond in a baseball field or those cool earrings you spotted at the mall the other day.

Rhombus definition: A rhombus can be defined as a diamond-shaped quadrilateral that has all four sides equal. But isn’t that a square? Yes, as a matter of fact, it is.

But how is a rhombus different? Well, unlike a square where all sides and angles are equal, the rhombus shape may show that it has all four sides equal, but only its opposite angles are equal.

## Properties of a Rhombus A rhombus, like all geometric shapes, has properties that are unique to it. These include:

• All four sides of a rhombus are equal.
• Opposite sides of a rhombus are parallel.
• Opposite angles of a rhombus are equal.
• Diagonals bisect each other at 90° or right angles.
• The sum of two adjacent angles is 180°.
• All rhombuses are parallelograms, but all parallelograms are not rhombuses.
• All rhombuses are not squares, but all squares are rhombuses.

## Formulae for a Rhombus

The formulae for rhombuses are defined for two features:

1. Area of a rhombus, where $$A = \dfrac{{d_1 d_2 }}{2}$$
2. Perimeter of a rhombus, where $$P = 4\times \text{side}$$

## Area and Perimeter of a Rhombus ### Area of a Rhombus

The area of a rhombus is defined as a product of the two diagonals divided by 2

 $$A = \dfrac{{d_1 d_2 }}{2}$$

Where $$d_1$$ and $$d_2$$ are the lengths of the diagonals.

### Perimeter of a Rhombus Since all four sides of a rhombus are equal, much like a square, the formula for the perimeter is the product of the length of one side with 4

 $$P = 4 \times \text{side}$$

## Angles of a Rhombus As mentioned in the properties of a rhombus, the sum of two adjacent angles is 180°.

So if one of the angles is 60°, then the adjacent angle will be 120°.

Also, opposite angles of a rhombus are equal, which means summing up the four angles will give you 360°, i.e. the number of degrees that can be measured in any quadrilateral.

## Diagonals of a Rhombus

One thing you should remember about the diagonal of a rhombus is that it always bisects at a 90° angle, which means that the two sides bisected will be the same length.

For example: if the length of a diagonal is 10 cm and the other diagonal bisects it, then it is divided into two 5 cm diagonals.

Unless the rhombus is a square, then the diagonals will have different values.

If you know the side of the rhombus and the value of certain angles, then you can determine the length of the diagonal.

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