A Rhombus is a quadrilateral projected on a two dimensional (2D) plane, having four sides which are equal in length and are congruent. It is also known as equilateral quadrilateral because all its four sides are equal in nature.
Let us see how to calculate the area of a rhombus.
For calculating the area of a Rhombus, we have three method, which we will discuss now-
Method 1 : Using Diagonals-
In the figure above, ABCD is a rhombus, having two diagonals, i.e. AC & BD.
Step 1- Find the length of diagonal 1, i.e. d1. It is the distance between A and C. The diagonals of a rhombus are perpendicular to each other making 4 right triangles when they intersect each other at the center of the rhombus.
Step 2- Find the length of diagonal 2, i.e. d2 which is the distance between B and D.
Step 3- Multiply both the diagonals, d1 and d2.
Step 4- Divide the result by 2.
The resultant will give the Area of a Rhombus ABCD.
Let us understand more through example-
Example: Calculate the area of a rhombus having diagonals equal to 6 cm and 8 cm.
Solution: Given that,
Diagonal 1, d1 = 6 cm
Diagonal 2, d2 = 8 cm
Area of a rhombus, A = (d1 * d2) / 2
= (6 * 8) / 2
= 48 / 2
= 24 cm2
Hence, Area of a rhombus is 24 cm2.
Method 2 : Using Base and Height
Step 1- Find the base and the height of the rhombus. The base of the rhombus is one of its sides, and the height is the altitude which is the perpendicular distance from the chosen base to the opposite side.
Step 2- Multiply the base and calculated height.
Let us see understand this through example:
Example: Calculate the area of a rhombus if its base is 10 cm and height is 7 cm.
Base, b = 10 cm
Height, h = 7 cm
Area, A = b * h
= 10 * 7 cm2
A= 70 cm2
Method 3. Using Trigonometry
Step 1- Square the length of any of the sides.
Step 2- Multiply it by Sine of one of the angles.
Let us see one example
Example- Calculate area of a rhombus if the length of its side is 2 cm and one of its angle A is 33.
Side a = 2 cm
Angle A = 33
square of side a = 2 * 2= 4 cm2
Area, A= s2 * sin (33)
A= 4 * 0.9999
A= 4 cm2
This was all about Area of rhombus. To learn more about area of quadrilaterals, such as Squares, area of Trapezium, download BYJU’S-The learning app.