Definition, Angles, Formulas, and Properties of a Rhombus

Are you finding difficulties in understanding the concept of a Rhombus? If yes, then you landed at the right place! The rhombus is a type of quadrilateral and usually has a diamond shape. It is one of the most commonly used Quadrilateral shapes in Mathematics and Geometry. Moreover, all the diagonals in a rhombus intersect with each other at a 90 degrees angle.

In this post, we are going to discuss and explain the definition, angles, formulas, and properties of a rhombus. Trust me; you will feel like you are having the easiest lesson of your life from a professional Math tutor while reading this post! But before going into the details of a rhombus, let us take a quick look at what is a quadrilateral!

What is a Quadrilateral?

A quadrilateral is a closed shape that has four angles enclosed with four verticals and four sides. Moreover, when you sum up all the interior angles of the quadrilateral, the answer would be equal to 360 degrees. There are further 6 types of quadrilateral:

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

Definition of Rhombus

A rhombus is defined as a type of quadrilateral, and a special type of parallelogram as well. All the opposite sides in a rhombus are parallel, and all the opposite angles are equal. Also, all four sides in a rhombus have equal and same length. Additionally, all the diagonals of a rhombus bisect each other at right angles.

Moreover, a Rhombus has three additional names; since a rhombus has a diamond shape, it is also called a ‘rhombus diamond’, Lozenge, or simply a ‘diamond’. In plural form, it is called rhombuses or rhombi.

Is Square a Rhombus?

All the sides of a rhombus are equal, right? Well, so does a square. Not only this, but all the diagonals bisect the opposite angles of the square. Also, a square has four right angles as well. Hence, a square can definitely be a type of Rhombus.

Angles of a Rhombus

We hope that you already know a rhombus has four interior angles, right? Now let us go through some significant facts about Rhombus angles:

  1. When we add up all the interior angles of a rhombus, we will get a sum of 360 degrees.
  2. In a rhombus, all the angles that are opposite to each other are the same.
  3. All the diagonals in a rhombus will bisect each other at the right angles.
  4. The adjacent angles of a rhombus are just additional.

Rhombus Formulas

There are two basic Rhombus formulas to find out these two things:

  1. Area of a rhombus
  2. The perimeter of a rhombus

Here is how you can find these both things:

Area of a Rhombus

The region that a rhombus covers in a two-dimensional plane is known as the area of a rhombus. Here is the formula to find it:

Area of a Rhombus = A = (d1 x d2)/2 square units

In this formula, d1 and d2 are known as the diagonals.

The perimeter of a Rhombus

The total length of the boundaries of a Rhombus shape is its perimeter. In simpler words, the sum of all the four sides of a rhombus is known as its perimeter. Here is the formula to find the perimeter:

The perimeter of a Rhombus = P = 4a units

In this formula, ‘a’ is the side.

Properties of a Rhombus

Now that we have gone through the definition, angles, and formulas, let’s move to the properties of a Rhombus! All these following properties are extremely important and you should know them by heart to fully absorb the concept of a Rhombus. Read on!

  1. All the sides of a Rhombus will always be equal.
  2. All the opposite sides of a Rhombus are parallel to each other.
  3. All the opposite angles of a rhombus will be equal.
  4. All the diagonals of a Rhombus will always bisect each other at right angles.
  5. All the diagonals bisect the angles.
  6. After summing up two adjacent angles, you will get a sum of 180 degrees.
  7. In a Rhombus, two diagonals can make four right-angled triangles.
  8. When you join a midpoint of the sides in a Rhombus, you can form a rectangle.
  9. If you join the midpoints from the half of the diagonal, you can form another Rhombus!
  10. You can not form any sort of circumscribing circle around a Rhombus.
  11. You can not form any inscribing circle inside a Rhombus.
  12. When you join the midpoints of all the four sides of a rhombus, you will form a rectangle. However, the width and length of that rectangle will be half of the diagonal. Eventually, the area of that rectangle will be half of the area of the rhombus.

Rhombus Solved Problems and Examples

Here are a few solved problems and examples related to the area and the perimeter of a Rhombus to help you have a better understanding!

Question no. 1

The diagonal lengths of a Rhombus (d1 and d2) are 7 cm and 15 cm. What is the area of this Rhombus?

Solution:

d1 = 7 cm
d2 = 15 cm
Now, we apply the formula:
A = (d1 x d2)/2 square units
A = ( 7 x 15)/2
A = 105/2
A = 52.5 cm2

Question no. 2

If the area of a Rhombus is 90 cm2, and the length of its longest diagonal is 15 cm. What is the diagonal of this Rhombus?

Solution:

Here, area of Rhombus = 90 cm2 and supposedly d1 = 15 cm.
Now, we apply the formula:
A = (d1 x d2)/2 square units
90 = (15 x d2)/2
121 = 7.5 x d2
or 7.5 = d2
Thus, the diagonal of this Rhombus is 7.5.

Question no. 3

If all the sides of a Rhombus are 8 cm, then what will be its perimeter?

Solution:

Side of the Rhombus = 8 cm
Now, we know that all sides are equal. Hence, we apply the formula:
Perimeter = 4 x side
P = 4 x 8
P = 32 cm
Hence, the perimeter of the Rhombus is 32 cm.

Frequently Asked Questions

Is square a type of Rhombus?

Not a type, but yes, a square can be a rhombus.

Can a Rhombus have 4 right angles?

No, a Rhombus can never have 4 right angles.

In a Rhombus, are all the angles equal?

No, only the opposite angles of a rhombus are equal.

Final Words

Now that you have gone through the entire post, we are sure your concepts about the definition, angles, formulas, and properties of a Rhombus are cleared. For more easy and detailed lessons, keep following and checking our blog or book one of our professional math tutors. You will surely find the answers to everything!

Find Top Tutors in Your Area

 
 
0 0 votes
Article Rating
Subscribe
Notify of
guest
0 Comments
Inline Feedbacks
View all comments
0
Would love your thoughts, please comment.x
()
x