AREA OF RHOMBUS FORMULA

Area of Rhombus Formula. PERIMETER AND AREA OF RHOMBUS 

If you are studying in any class or preparing for any entrance exam then you must learn Geometry. Rhombus is an essential part of Geometry. In the examination there is two or three questions are always comes from Geometry section. So you need to master in this section, you can’t skip it.

WHAT IS A RHOMBUS?

Rhombus is a flat shape that means it is a 2-dimensional figure. 

Properties:

• All sides have equal length 
• It is a parallelogram so all the opposite sides are parallel.
• As opposite sides are of equal length and parallel, then that signifies equal opposite angles. 
• The diagonal bisect each other perpendicularly.
• Also known as a diamond shape.

The following is the shape of the rhombus with 2 diagonals D1 and D2. 

Some point you should remember – 

Firstly the diagonal divides the rhombus into 2 congruent triangles. 

Therefore the two triangles have the same area. 

Rhombus is a 2-dimensional figure with all the sides having equal length . A rhombus is also a parallelogram. The area of the rhombus can be calculated in three ways. First, the base times height method. Secondly, the diagonal method. And thirdly, using trigonometry.

A rhombus can also be found in a lot of things around us such as the windows of a car, a kite, earrings of rhombus shape and a lot more! It can also be found in the structure of a building, mirrors, and can be applied while selecting the baseball field. Hence, it is very important to study in-depth about rhombus.

Methods to calculate the area of RHOMBUS 

1. The ‘base times height’ method 

Area = base (side) x height (altitude)

2. The ‘diagonal’ method 

Another simple method of calculating the area is using the length of diagonals. 

In the above-shown figure, D1 and D2 are the 2 diagonals. 

To calculate the area you have to multiply both the diagonals and divide it by 2. 

Area = D1 X D2 / 2

Solved Example :-

Question:- Find out the area of Rhombus having diagonals equal to 20 cm and 28 cm.

Solution :- Given that,

Diagonal 1, D₁ = 20 cm

Diagonal 2, D₂ = 28 cm

Area of Rhombus, A= (D₁ * D₂)/2

= (20*28)/2

= 560/2

=280 cm²

3. Using Trigonometry

Some people even use trigonometry to derive a handy formula. 

Area = S²sin a 

S is the length of any side, a is any interior angle and sin is the sine function.

Now let us consider some examples to apply these formulas. 

Perimeter of rhombus 

Perimeter = 4 x length of each side 

Solved example 

Question: Find out the perimeter of the rhombus having side 6cm. 

Answer:  

We know, all the sides of the rhombus are equal 

So length of each side = 6 cm 

Perimeter = 4 x length of each side 

                   = 4 x 6 cm 

                  = 24 cm