Area of Rhombus

The area of a rhombus is the amount of space enclosed by a rhombus in a two-dimensional plane. A rhombus is a special type of parallelogram in which all sides are equal to each other. The shape can be differentiated from a square through the measure of its internal angle. The internal angle of a rhombus need not be a right angle specifically. The area of a rhombus can be calculated in different ways, depending on the parameters known to us. Let us learn more about the area of a rhombus, and the area of rhombus formula in this article.

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. It depicts the total number of unit squares that can fit into it and it is measured in square units like cm², m², in², and so on. Rhombus is a parallelogram in which the opposite sides are parallel, the opposite angles are equal, and the adjacent angles are supplementary. The following are the properties of a rhombus.

• A rhombus is a quadrilateral because it has 4 sides.
• The diagonals of a rhombus bisect each other at right angles.
• The diagonals of a rhombus are angle bisectors.
• The area of a rhombus can be found in different ways: using base and height, using diagonals, and using trigonometry.

The area of rhombus formula depends upon the parameters known to us. There are different formulas based on different parameters as given below:

• Formula using Base and height: Area of a Rhombus = base × height
• Formula using diagonals: Area of rhombus = (diagonal₁ × diagonal₂)/2
• Formula using trigonometry: Area of a Rhombus = side² × sin(A)

Let us understand the area of rhombus formulas in detail and use them to find the area of a rhombus now.

Formula for Area of Rhombus with Base and Height

Rhombus is a parallelogram. We know that the area of a parallelogram is calculated by multiplying its base and height. The same rule is applied to the rhombus as well.

Area of a Rhombus = base × height

Let us find the area of a rhombus using this formula.

Example: Find the area of a rhombus in which the side length is 7 inches and the height of the rhombus is 10 inches.

Solution: The side length of a rhombus = 7 inches, height = 10 inches.

As we know, Area of rhombus = base × height

⇒ Area of rhombus = 7 × 10

⇒ Area of rhombus = 70 inches²

Formula for Area of Rhombus with Diagonals

The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula which is used to find the area of a rhombus using diagonals is given as,

Area = (d₁ × d₂)/2, where, d₁ and d₂ are the diagonals of the rhombus.

Observe the Rhombus ABCD given above in which E is the point of intersection of two diagonals. The other points to be noted about this rhombus are given below:

• All four sides of the rhombus are congruent. Here, AB = BC = CD = DA
• The two diagonals are AC and BD.
• The opposite angles in the rhombus are equal. Here, ∠A = ∠C and ∠B = ∠D

The area of the rhombus ABCD = Area of ∆ ADC + Area of ∆ ABC

Area of the rhombus = 2 × Area of ∆ ABC ---Equation (1) (∵ ∆ ABC congruent to ∆ ADC)

Area of ∆ ABC

= 1/2 × Base × Height

= 1/2 × AC × BE

= 1/2 × AC × 1/2 × BD (∵BE = BD/2)

= 1/4 (AC × BD) --- Equation (2)

Area of the Rhombus ABCD

Area of rhombus = 2 × 1/4 × AC × BD = 1/2 × AC × BD (From (1) and (2))

⇒ Area = 1/2 × diagonal 1 × diagonal 2

∴ Area of a Rhombus = 1/2 × diagonal 1 × diagonal 2

Formula for Area of Rhombus When Side and Angles Are Known

We apply the concept of trigonometry while calculating the area when sides and angles are known. We can use any angle because either the angles are equal or they are supplementary, and supplementary angles have the same sine. Area of a rhombus using side and angle is given as,

Area of a Rhombus = side² × sin(A), where 'A' is an interior angle.

Let us use this formula in the following example to find the area of a rhombus.

Example: What is the area of a rhombus if the length of its side is 4 yards and one of its angles A is 30º?

Solution: As we know, the area of a rhombus = s² × sin(30º)

Area of rhombus = s² × sin(30º) = 4² × 1/2

⇒ Area of rhombus = 16 × 1/2 = 8 sq yards

Tips and Tricks

• Remember that the height is not the same as the length of the side of a rhombus.
• The area of a rhombus can be found in three ways: when diagonals are given, when an angle and a side are given, when base and height are given.
• Use the Pythagoras theorem to find the second diagonal if we know the length of one diagonal and the side length.

What is the Area of Rhombus?

The area of a rhombus is the total amount of space enclosed by a rhombus in a two-dimensional plane. It is expressed in square units like cm², m², in², and so on.

What is the Area of a Rhombus Formula?

The area of rhombus formula depends upon the parameters known to us. There are different formulas based on different parameters as given below:

• Formula using Base and height: Area of a Rhombus = base × height
• Formula using diagonals: Area of rhombus = (diagonal₁ × diagonal₂)/2
• Formula using trigonometry: Area of a Rhombus = side² × sin(A)

What is the Difference Between Area of Rhombus and Area of Square?

The area of a square is calculated using the formula, Area of square = s × s, where 's' is the side length of the square. Whereas, the area of a rhombus is calculated using the formula, area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

What is the Difference Between Area of Rhombus and Area of Rectangle?

The area of a rectangle is calculated using the formula, Area of rectangle = l × b, where 'l' is the length of the rectangle and 'b' is the breadth of the rectangle. Whereas the area of a rhombus is calculated using the formula, area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals. Another way to find the area of a rhombus is using its base and height with the help of the formula, Area of rhombus = base × height.

What is the Difference Between Area of Rhombus and its Perimeter?

• The perimeter of a rhombus is the total length of its boundary and it is calculated by adding the length of all its 4 sides.
• The area of a rhombus is the space covered by the rhombus. The area of a rhombus can be calculated using its base and height with the help of the formula, Area of rhombus = base × height. Another way to find the area of a rhombus is using its diagonals. So, this formula is expressed as, Area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

What is the Use of Area of a Rhombus Calculator?

The area of a rhombus calculator is an online tool with the help of which we can easily evaluate the area of rhombus in seconds. To determine the value we need to enter the specific parameters such as the value of the diagonals. Try Cuemath's online rhombus area calculator for quick calculations and solve your problems related to the area of the rhombus within seconds.

What is the Altitude if the Area of Rhombus is Given?

If the area of a rhombus is given, we can find the altitude with the help of the base length. We can use the formula, Area of rhombus = base × height. After substituting the value of the area and the base length, we can find the height which is also known as the altitude.

What is Area of Rhombus Formula when Side and Diagonal is Given?

We can find the area of a rhombus when the side and diagonal are given. In this case, we can find the length of the other diagonal using the Pythagoras theorem. Then, we can use the formula, Area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.