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A rhombus is a quadrilateral in Euclidean plane geometry, whose four sides have the same length. Often, a rhombus is called a diamond. Each rhombus is simple and is a special case of a kite and a parallelogram. A square is a rhombus with right angles. In a way, all squares can be considered rhombuses but every rhombus is not necessarily a square. Here, the concepts and formulas of a rhombus, like the formula of the area of a rhombus, are discussed in detail.

When dealing with Rhombus, the first question a student gets is How to find the area of a rhombus? Since we have a different formula to find an area of the rhombus.

Let’s discuss all formula of the rhombus briefly:

Based on Side of the Rhombus Formula

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Area of rhombus when side and height is given

A = a * h

Where a = length of sides of the rhombus

h = height.

Based on Diagonal of Rhombus Formula

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Area of Rhombus when diagonal of rhombus formula is given:

\[A = \frac{1}{2} \times d_{1} \times d_{2}\]

Where d_{1} and d_{2} are the diagonals of the rhombus, the formula of diagonal of the rhombus is given as follows:

\[d_{1} = \sqrt{4a^{2} - d_{2}^{2}}\]

\[d_{2} = \sqrt{4a^{2} - d_{1}^{2}}\]

Based on the Perimeter of the Rhombus Formula

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Rhombus area and perimeter formula are given:

A= 2*a*r

Where a = length of sides of the rhombus

r = radius of a circle inscribed in the rhombus

P= perimeter of rhombus= 4*a

Semiperimeter= 2*a

Based on Height and Vertex Angle

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Area of Rhombus when height and vertex angle is given:

\[A = \frac{h^{2}}{sin \alpha}\]

Where h= height and α = vertex angle

1) Find the area of the rhombus when the side is 4 cm and the height is 6 cm.

Ans: Area of rhombus when side and height is given,

A = a * h

From question a = 4cm and h = 6cm. Substituting these values we get,

A = 4 * 6 = 24 cm2

2) The diagonals of the rhombus are given as 8 cm and 12 cm. Find the area of the rhombus.

Ans: Area of rhombus when diagonals are given,

\[A = \frac{1}{2} \times d_{1} \times d_{2}\]

From question d1=8 cm and d2=12 cm. Substituting these values we get,

\[A = \frac{1}{2} \times 8 \times 12 = 48\] cm2

The name “Rhombus" derives from the word “Rhombos” used in Ancient Greece. It means a piece of wood whirled to make a roaring noise on a string. We see rhombus-shaped figures every day today, in various spheres of life, hence it is very important to learn and understand the concepts of this shape.

FAQ (Frequently Asked Questions)

Q1: What is the Difference Between a Rhombus and a Square?

Ans: A rhombus is a polygon with four sides, and all the sides are equal in length. The opposite angles of a rhombus are identical, and at 90 degrees, the diagonals bisect each other.

A square is also a four-sided polygon that has the same length on all its sides, and all the angles are equal to 90 degrees. Also, the length of the diagonals is equal.

Q2: Are Diagonals Equal in Rhombus?

Ans: A rhombus diagonals are not equal. It is called a square when the diagonals of a rhombus are identical. A square is a special type of rhombus where the four angles are 90 degrees, making all diagonals the same.