Rhombus and its Properties

Do you wonder what shape will form if you tilt the square by 45°? Nevertheless, a rhombus is different from this. Let’s learn more about Rhombus and its properties of Rhombuses.

A rhombus is a form of quadrilateral in Euclidean geometry. It is a specific case of properties of a parallelogram, in which the diagonals cross at 90 degrees. The basic attribute of the Rhombus is its unique shape. The shape of a rhombus is similar to that of a diamond. As a result, it is also known as a diamond. In a rhombus, look for symmetry lines for its proper identification.

The Rhombus resembles the shape of a quadrilateral. It has four vertices and four sides enclosing four angles, exactly like most other quadrilaterals such as rectangles, squares, and so on. It, however, is not all. There is a lot more to learn about this fascinating 2D shape which is an important component of mathematics.

It is also one of the key courses that follow us from school to university. So, let’s learn everything there is to know about Rhombus, including its qualities, angles, sides, and two diagonals. But first, let’s have an understanding of quadrilaterals.

What do you understand by a Quadrilateral?

As the name indicates, quad means four. Before we go into the Rhombus and its attributes, do you know what a quadrilateral is? It is a polygon with four sides and four vertices with four angles. The total sum of a quadrilateral’s internal angles equals 360 degrees.

There are six different sorts of quadrilaterals in geometry:

1. Trapezium
2. Square
3. Rectangle
4. Parallelogram
5. Rhombus
6. Kite

What is a Rhombus?

A rhombus is a four-sided figure (quadrilateral) that is a particular case of a parallelogram. The opposite sides of a rhombus are parallel, and the interior angles are equal.

Furthermore, all of a rhombus’s sides are the same length, and the diagonals intersect each other at angles perpendicular to each other. A rhombus can alternatively be referred to as a diamond or a rhombus diamond because of its unique shape. Rhombi or rhombuses are the plural representation of Rhombus.

Is a square a Rhombus?

A square, like a rhombus, has all of its sides equal. In addition, the square’s diagonals are perpendicular to one another and bisect the angles opposite to each other. As a result, a square is a kind of Rhombus.

What are the facts regarding the Angles of a Rhombus?

One might argue whether Rhombus is a square or not. However, although a rhombus is not a square, a square is a type of Rhombus. It makes it slightly different from the square shape.

Following are some important facts regarding the angles in a rhombus.

• There are four interior angles in a rhombus
• The sum of all the interior angles in a rhombus is 360 degrees
• Interior opposite angles are equal to each other
• In a rhombus, adjacent angles are supplementary to each other
• Diagonals inside a rhombus intersect each other perpendicularly at right angles
• The diagonals bisect each angle formed between them

Angles of Rhombus

Any rhombus has four angles, with the opposite ones being equal. Furthermore, this shape is made up of diagonals that intersect each other at right angles. To put it another way, each diagonal of a rhombus divides the other into two equal pieces, and the angle generated at their intersection points is 90 degrees.

The Rhombus has four interior angles, and as the sum of two alternate sides is 180 degrees, the overall sum of the Rhombus’ four interior angles is 360 degrees. The diagonals also bisect the Rhombus’s opposite angles, dividing the Rhombus into two separate triangles that are congruent to each other.

State the Properties of Rhombus

Because it has all of the qualities of a parallelogram, a rhombus is considered one of the exceptional parallelograms.

The symmetrical lines of a rhombus are its two diagonals. A line that separates an object into two identical halves is known as an axis of symmetry. Both sides of the object are reflected in a mirror-like reflection. Over both of its diagonals, a rhombus is said to exhibit reflection symmetry. Some of the parallelogram’s general qualities are as follows:

• Opposite angles inside a parallelogram are equal or congruent
• In a parallelogram, the opposing sides are parallel to each other
• The opposite sides are equal in length
• Each diagonal bisects the other one
• The sum of two consecutive angles in a parallelogram is 180 degrees

The diagonal of a rhombus should be remembered because, in addition to bisecting each other at right angles, the two diagonals bisected will also be the same length.

Like other geometric shapes, the properties of rhombus are particular to it. The properties of rhombus are shown in the table below. 

Properties of Rhombuses	References
A rhombus has congruent sides (equal).	In this case, AB = CD = DA = BC
The perpendicular bisector of each of the two diagonals in a rhombus is the diagonal that it bisects at 90 degrees.	Here, diagonals DB and CA form a 90° angle with one another.
The opposing sides are parallel, and the opposing angles are equal.	CD || AB and BC || AD
Angles adjacent to one another add up to 180 degrees.	∠A + ∠B = 180°   ∠B + ∠C = 180°   ∠C + ∠D = 180°   ∠A + ∠D = 180°

For example, if a diagonal is 12 cm long and is bisected by another diagonal, it is divided into two 6 cm pieces. One can calculate the length of the diagonal if one knows the side of the Rhombus and the values of certain angles.

How to identify a Rhombus?

A rhombus is a quadrilateral. It is shaped like a diamond and has equal sides on all sides. In our daily lives, we see rhombus-shaped figures. A diamond, a kite, and other real-life examples.

How do find Rhombus in daily life?

Even though one might not notice it, at all times, the Rhombus shape is present in front of our eyes. From the kite shape to the diamond shape. The application of Rhombic shape may be seen everywhere, from the design of a kite to the shape of jewellery.

The shape of a Rhombus is so common that it can be found in shop signs, road signs, key chains, tiles, baseball fields, and so on. This shape can also be seen in several well-known architectural structures around the world.

The Rhombic shape is so popular because it is symmetrical and has a very attractive and pleasing shape. Because all four sides of the Rhombus are equal, the figure is also geometrically viable.

Rhombus Formulas

The formula of a rhombus deals with two main parameters. These are – the perimeter and area.

• The expression gives the formula for the area of a rhombus-

A = ½ × d1 × d2

Here, d1 and d2 are the diagonals of the Rhombus.

• The formula for the perimeter of the Rhombus is given by-.

P = side + side + side + side

Since the four adjacent sides of a rhombus are equal,

P = 4 × side

What is the Perimeter of a Rhombus, and how to calculate it?

A perimeter of a shape refers to the total length covered by all the sides of that shape. In other words, it is better defined as a boundary that restricts a figure and confines its outlines.

For a rhombus, its perimeter will be the sum of all its four sides that confines its countries. So, the perimeter will be :

P = side + side + side + side

P = 4 × side

For example, as it is known, all the sides of a rhombus are equal. So, if one side = 7 cm

Then, the perimeter will be:

P = 7 + 7 + 7 + 7

P = 28 cm

What is the area of a Rhombus, and how to calculate it?

An area of an object is defined as the total space occupied by that particular object. In this case, the area of a rhombus is the entire space occupied by the four sides and everything between them.

The area of a rhombus is given by the following equation:

A = ½ × d1 × d2

Here, d1 and d2 refer to the diagonals of a rhombus.

For example: if the diagonals of a rhombus are 12 cm and 6 cm. Then, is the area will be:

A = ½ × d1 × d2

A = ½ × 12 × 6

A = 36 cm²

What are the various other Properties of Rhombus?

For a quick review of the properties of rhombus, read the following points.

• All four sides are the same length.
• The opposite sides are parallel.
• Opposite interior angles are the same.
• At right angles or 90 degrees, diagonals bisect each other perpendicularly.
• The diagonals of a rhombus intersect its opposite angles.
• The total of two neighboring angles, i.e. 180°, is supplementary.
• A rectangle is formed by uniting the midpoints of the sides of a rhombus.
• There is no possibility of an inscribing circle within a rhombus.
• Two congruent equilateral triangles are created when the shortest diagonal side of a rhombus equals one of its sides.

Summary

To summarize, the Rhombus’ shape is symmetric along its diagonals, which means that the area on both sides of the diagonals is equal. That is, dividing the Rhombus from one of its diagonals yields symmetric objects with the same area and perimeter. The Rhombus’ symmetric feature is mostly due to the presence of the two diagonals that are equal and bisect each other. The properties of rhombus are an important concept in mathematics and geometry.

Solved Rhombus Examples 

Example 1: David has drawn a rhombus with two diagonals that are, respectively, 5 units and 10 units long. He asks Linda, his sister, to guide him to the location. Can you help Linda to find the solution? 

Solution: 

 Given: 

 The diagonal values are d1 = 5 units and d2 = 10 units. 

A = (d1 × d2)/2 

A = (5×10)/2 

A = 25 square meters 

The rhombus has a surface area of 25 square units. 

Example 2: Sam and Victor were playing a game of hopscotch when they noticed a tile at the playground that was shaped like a rhombus. The tile was 15 units long on either side. Can you help Sam and Victor in finding the tile’s perimeter? 

Solution: 

Given: 

The tile is 15 units long. 

All four sides of a rhombus are equal to 15 units since all its sides are equal. 

4 units for the perimeter, 4 units for each side, and 15 units total. 

The tile’s perimeter is 60 units, thus that’s the answer. 

Frequently Asked Questions

1. What are the qualities of a rhombus?

Ans. A rhombus has four equal sides, and two of those sides are perpendicular to the other two.

Rhombuses are named for their shape: a rhombus can be thought of as a diamond cut in half.

2. What is a real-life example of a rhombus?

Ans. A rhombus is a four-sided shape with all sides equal in length and all angles equal. The most common example of a rhombus is a diamond. The shape of a diamond is a rhombus because all of its edges are the same length and all of its angles are equal.

3. What do all rhombuses have in common?

Ans. Rhombuses are all about corners. They have four of them, and they’re all 90 degrees. Rhombuses are also parallelograms, which means that they have two pairs of parallel sides.

4. What are the facts about rhombus?

Ans. -A rhombus is a quadrilateral with four equal sides and four equal angles.

-Rhombuses have many different names, including parallelograms and kite shapes.

-A rhombus can be a square if all of its sides are square.

5. What are the properties of rhombus?

Ans. A rhombus is a parallelogram that has four equal sides. The angles of a rhombus are always equal to one another. It is also a special case of a parallelogram, as it has all sides equal. In addition, the diagonals of a rhombus are perpendicular to each other.