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April 8, 2025Rhombus is a two-dimensional quadrilateral with all its sides equal. Rhombus is shaped like a diamond and there are many ways to calculate its area. It is a quadrilateral with two sets of parallel sides, equal opposite sides, and equal angles. It is also called an equilateral quadrilateral because it has equal four sides. When all four angles of a rhombus are 90 degrees, it can be called a square. In this article, there will be an in-depth discussion on rhombus and its properties. Follow this page to understand all the concepts associated with the topic of rhombus.
We can find a large number of examples of rhombus around us. The shape of a rhombus is similar to that of a diamond and hence it is often referred to as a diamond. It is important for students to understand what is a quadrilateral in order to understand the concept of rhombus. A polygon that contains four sides with four angles and vertices is considered to be a quadrilateral. There are six different types of quadrilaterals, trapezium, rectangle, square, parallelogram, kite and rhombus. This article will focus on rhombus and help students understand the difficult concepts associated with rhombus.
The word rhombus is derived from the Greek word “rhombus” which means a piece of wood whirled on a string to create a roaring noise, and this word was eventually derived from the Greek verb “rhembo” which means to turn round and round.
Rhombus is parallelogram where, no side is bigger or smaller than the other. The opposite sides of a parallelogram are parallel and all its sides are equal. Rhombus is often referred to as the subset of a parallelogram. The only difference between a square and a rhombus is that all angles of a square are right angles however, it is not necessary for the angles of a rhombus to be right angle. Any rhombus that has its four angles as 90 degrees will be referred to as a right angle. Hence, every square is a rhombus, but all rhombuses are not a square.
1. All sides of a rhombus are equal i.e.,
2. Diagonals bisect each other at
3. Opposite sides are parallel in a rhombus i.e.,
4. Opposite angles are equal in a rhombus i.e.,
5. Adjacent angles add up to
The area of a rhombus can be interpreted as the amount of space enclosed by a rhombus in a
Area of rhombus has different formulas in different cases, and the most commonly used are given below:
Using diagonals | Area |
Using base and height | Area |
Using trigonometry | Area |
Where,
1.
2.
3.
4.
5.
Half of the product of diagonals provides us with the area of the rhombus. Area
Where
Let
The diagonals bisect each other at
So,
So, the area of
Hence, area of rhombus
So, the area of rhombus
When the length of base (side) and height of the rhombus are given, the area of a rhombus with a side is easy to find. A simple formula can be applied, and the area of a rhombus with a side is calculated. If the base (side) of the rhombus is named
Area of Rhombus
In some cases where height is unknown, but the base and one of the angles is known, the area can be calculated by multiplying the square of the base with the sine of that angle. If the base of the rhombus is
Area of rhombus
Let
The diagonals bisect each other at
So, the area of rhombus
So, the area of Rhombus
The vector concept is also used to calculate the area of the rhombus. Since all rhombuses are parallelograms, the area of the rhombus in vector form is given by
Area of rhombus
Question 1: Evaluate the area of a rhombus, if its base is
Answer:
Given,
Base,
Height,
Area,
Question 2: Evaluate the area of the rhombus having diagonals
Answer:
Given that,
Diagonal
Diagonal
Area of rhombus
Question 3: Find out the area of a rhombus if the length of its side is
Answer:
Given,
Side or base
Area of rhombus
Question 4: Calculate the area of the rhombus having side equal to
Answer:
So ,
Let
So,
In
Therefore,
Now, area of rhombus
Question 5: The building floor consists of
Answer:
In each rhombus-shaped tile, the length of the diagonals is
Therefore, the area of each tile
Therefore, the area of
For
For
Question 6: If the area of a rhombus is
Answer:
Area of rhombus
That is,
On putting
So, the length of the other diagonal is
A rhombus is a quadrilateral whose all sides are equal and opposite sides are parallel. Rhombus is a subset of a parallelogram and it can be square in a special case. The properties of the rhombus and the area of the rhombus formula are widely used to solve real-life problems. Every formula is derived from basic geometrical concepts.
Q1. Is the topic rhombus important from the exam point of view?
Ans: From the exam perspective, a student needs to cover all the topics. Selective study will not be helpful at all.
Q2. Is rhombus a parallelogram?
Ans: Yes, rhombus is a parallelogram.
Q.3. What are the
Ans: The most commonly
1. All sides of a rhombus are equal.
2. Diagonals bisect each other at
3. Opposite sides are parallel, and opposite angles are equal in a rhombus Adjacent angles add up to
Q.4. What is the difference between rhombus and square?
Ans: Although a rhombus and a square have all their sides equal, they are not the same. All interior angles of the square are
Q.5. What does a rhombus look like?
Ans: A rhombus looks like a diamond, symmetrical kite, Kaju Katli, etc.
Q.6. Is every square a rhombus?
Ans: Yes, every square is a rhombus as the rhombus is a quadrilateral having all its sides are equal and opposite sides are parallel. So a square is a special case of rhombus where all its angles are also
Q.7. Are the diagonals of the rhombus equal?
Ans: Generally, the diagonals of the rhombus are not equal, but if the rhombus is a square, its diagonals are equal. So in a particular case, it can be equal.
Q.8. Are all rhombuses parallelograms?
Ans: Yes, opposite sides are parallel and equal in a parallelogram. So, all rhombuses are parallelograms as all sides of a rhombus are equal, and opposite sides are parallel.
Q.9. How to find the area of a rhombus if the base and height are given?
Ans: Area of a rhombus (if base and height are known)
Now that you are provided with all the information on the area of the rhombus and we hope this detailed article is helpful to you. Follow Embibe to get more updates on Mathematics and other subjects. We also have articles on competitive exams. Check them out!
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