Area of Rhombus

The area of a rhombus in a two-dimensional plane is defined as the amount of space surrounded or encompassed by it. A rhombus is a form of parallelogram in which all of the sides are equal. The internal angle of a rhombus can be used to distinguish it from a square. The internal angle of a given rhombus does not have to be a straight angle. Depending on the characteristics we have, we can compute the area of a rhombus in a variety of methods.

Area of rhombus:-

The area of a given 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, etc). The Rhombus is also a parallelogram with the opposite sides parallel, the opposite angles equal, and the adjacent angles supplementary. The mentioned  properties are used to define a rhombus.

• The sides of a rhombus are of the same length, making it an equilateral quadrilateral.

• Diagonals in a given  rhombus bisect each other at right angles.

• Angle bisectors are the diagonals.

• The area of a rhombus can be calculated in a variety of ways, including utilising the base and height, diagonals, and trigonometry.

Area of rhombus formula:-

Depending on the characteristics we know, many formulas can be used to compute the area of a rhombus. The following are the several formulas used to calculate the area of a rhombus:

Area of rhombus when base and height of rhombus are given:-

Rhombus is a type of parallelogram. We can calculate the area of a parallelogram by multiplying the base and height in square units. The rhombus is treated in the same way.

Area of the rhombus = base x height sq. units

Ex:- Find the area of the rhombus whose base is 5 cm and height is 7 cm?

We have the base of rhombus (b)=5 cm

And the height of the rhombus (h)=7 cm

Area of the rhombus=b*h= (5*7) cm²= 35 cm²

How to get the area?

Step 1:- Note down the base and height of the rhombus. And height will be the perpendicular distance from chosen base to the opposite side of a rhombus, whereas the base is one of its sides.

Step 2:- Multiply the height and base of the rhombus.

Step 3:-Write down the result with  square unit.

AREA OF RHOMBUS USING DIAGONAL:-

The area of the rhombus is equal to the half of the product of the length of the diagonals. The following is the formula for calculating the area of a rhombus using diagonals:

Area of the rhombus= (d1* d2)/2 square units, d1 and d2 are the diagonals of the rhombus.

Ex:- Find the area of the rhombus whose diagonals are 10 cm and 8 cm.

We have the diagonals of the rhombus, one is (d1) 10 cm and other is (d2) 8 cm.

Area of the rhombus = (d1*d2)/2= (10*8)/2= 40 cm².

How to find the area?

Step1:- Note down the diagonals of the rhombus as diagonal 1 (d1) and diagonal 2 (d2).

Step2:- multiplying both the diagonal and make it half or multiply by ½.

Step3:- Write down the answer in square units.

AREA OF THE RHOMBUS USING SIDE AND ANGLE OF THE RHOMBUS:-

When the sides and angles are known, we will use the formula of trigonometry to calculate the area of the rhombus. Because the angles are either equal or supplementary, and supplementary angles have the same sine, we can utilise any angle. The area of a rhombus is calculated using side and angle as follows:

Area of a Rhombus = side² × sin(A) sq. units, where ‘A’ is the interior angle of the rhombus.

Ex:- What is the area of the rhombus if the length  of its side is 5 cm and one of its angles is 30°.

The length of the rhombus is 5 cm and one of the angles is (A) 30°.

Area of the rhombus= side² × sin(A) = 5² * sin30 = 25*½=12.5 cm² .

How to find the area?

Step1:- Note down the length of the side.

Step2:- Squaring the length of the side.

Step3:-  Multiplying step2 with the sine of the angles and we get the result.

CONCLUSION: –

A given Rhombus is a quadrilateral that has four edges and four corners and all 4 edges are equal in length. All the rhombuses have parallelograms, which mean that the adjacent edges are parallel to each other. The interesting point to note here is that a given rhombus whose corners are at the 90 degree – right angle is known as a square.

A rhombus is the parallelogram with four sides that are all the same. It isn’t required to have right angles. The area of a rhombus can be calculated using three different formulas.we can calculate the area of the rhombus by using the base and height of the rhombus , by using the diagonals and the sides and angle of the triangle.