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# Rhombus|Definition & Meaning

**Definition**

A **rhombus** is a two-dimensional (or flat), closed shape with four equal-length straight sides such that the opposite angles are equal and the opposite sides are parallel to each other. In other words, it is a parallelogram with all four sides equal. A square is a type of rhombus where all the interior angles are right angles.

Figure 1 below shows a Rhombus.

Figure 1 – Representation of a rhombus.

**Rhombus as Quadrilateral**

A **quadrilateral** is a rhombus shape. It is a parallelogram with identical sides and diagonals connecting at 90 degrees. This is the rhombus’s most crucial characteristic. A rhombus resembles a **diamond**. As a consequence, it is sometimes referred to as a diamond.Â

A rhombus is a closed planar two-dimensional figure. Due to its distinguishing characteristics, it is classed as an unusual parallelogram and a quadrilateral. Because all of its sides have the same length, a rhombus also was known as just an **equilateral quadrilateral**.

The term ‘rhombus’ is derived from the ancient Greek term ‘rhombos,’ which refers to something that spins.

A **quadrilateral** is a closed polygon with four sides and four vertices enclosing four angles. The total of a quadrilateral’s internal angles equals 360 degrees. The quadrilateral is classified into six types:

- Parallelogram
- Rectangle
- Kite
- Trapezium
- Rhombus
- Square

**Rhombus, Parallelogram, and Square**

A **rhombus** is a particular parallelogram since it fulfills the definition of a rectangle as a **trapezoid** with a second pair of parallel sides. A rhombus, like a cube, has four equal sides. As a response, it’s often referred to as a diagonal square. Examine the picture below to see how the rhombus relates to the trapezoid & square.

Figure 2 below shows a difference in Rhombus, Parallelogram, and Square.

Figure 2 – Difference between a rhombus and other polygons.

Due to its four equal sides, a square is a specific example of a rhombus. All of the angles in a square were right angles. However, not all of the angles in a rhombus must be right angles. As a result, a rhombus containing right angles is a square.

**As a result, we may conclude:**

Parallelograms are all rhombi or rhombuses, although not all parallelograms are rhombuses.

Every **rhombi **or rhombus is not a square, but every square is a rhombus.

Three other names can also know a rhombus:

- Lozenge
- Diamond
- Rhomb

**Rhombus Angles**

One thing to remember regarding a rhombus’ diagonal is that, despite bisecting one another at 90 degrees, the two diagonals crossed will be the same length.

For example, if a diagonal is 10 cm long and another diagonal bisects it, it is split into two 5 cm pieces. You can calculate the length of a diagonal if you know the side of a rhombus and the values of specific angles.

The following are some exciting rhombus angle facts:

- The inner angles of a rhombus are four.
- The total of a rhombus’ internal angles equals 360 degrees.
- A rhombus’s opposing angles are congruent with each other.
- The adjoining angles are extraneous.
- Diagonals in a rhombus intersect at right angles.
- The diagonals of both rhombi bisect these angles.

Figure 3 bellows shows the angles of a rhombus.

Figure 3 – Representation of rhombus and its angles.

**A Rhombus’s Properties**

A rhombus is referred to as a unique parallelogram since it possesses all of the features of a parallelogram. Two diagonals serve as symmetry lines in a rhombus.

A **symmetrical axis **is a distinct line that splits an item in half. It generates a reflecting surface image of the item’s two sides. A rhombus’ diagonals all have reflection symmetry.Â

### Characteristics of a Rhombus

The characteristics of a rhombus are listed below:

- The rhombus has equal sides on all sides.
- A rhombus’s opposite sides are parallel.
- A rhombus’s opposite angles are equal.
- Diagonals in a rhombus
**intersect**at right angles. - Diagonals bisect a rhombus’ angles.
- The combination of two angles that are adjacent equals 180 degrees.
- You will receive a rectangle when you link the midpoints of the sides.
- When you combine the center point of half the diagonal, you obtain another rhombus.

There are also a few more advanced properties on its relationships with other geometrical shapes:

- There cannot be a constraining circle around a rhombus.
- There could be no
**engraved**circle within a rhombus. - The
**midpoints**of four sides will be linked to form a rectangle, and the length and breadth of a rectangle will be the value of a major diagonal, resulting in a rectangle with half the area of the rhombus. - Two congruent, evenly spaced triangles are generated when the longer diagonal equals one of the sides of a rhombus.
- When the rhombus is rotated around any side as that of the
**axis of rotation**, you will receive a cylindrical surface with a convex conical at one end and a concave cone at the other. - Whenever the rhombus is rotated about the line connecting the center point of the different sides as that of the axis of rotation, you will see a cylinder surface with concave cones on both ends.
- When the rhombus revolves around the longer
**lateral**axes of rotation, you will get solid with two cones joined to their bases. In this scenario, the greatest diameter of the block is equal to the rhombus’s shorter diagonal. - When the rhombus revolves around the longer diagonal as that of the axis of rotation, you will get a solid containing two cones linked to their bases. In this scenario, the greatest diameter of the block is equal to the
**rhombus’s longer diagonal**.

**The Rhombus Area**

The rhombus’ area is the territory it covers in a 2-dimensional surface. The formula for area is the product of the rhombus’ diagonals divided by two. It can be written as:

\[ A = \dfrac{(d1 \times d2)}{2} \times \text{square units} \]

**Example of a Rhombus**

When they noticed a rhombus-shaped tile, Sam and Victor played hopscotch at the playground. Each side of a tile was ten units long. Can you assist Sam and Victor in determining the tile’s perimeter?

**Solution**

The tile’s length is ten units.

Because a rhombus has equal sides, all four sides were equivalent to 15 units.

Perimeter = 4, side = 4, ten = 40 units

The perimeter of a tile is 40 units.

*All Images are made using GeoGebra.*