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Home >> Rhombus >> Area of Rhombus >> Area of Rhombus
Before you study how to calculate area of rhombus, you are advised to read:
What is Rhombus ?
How to find Area of Triangle ?
Formula to calculate Area of Rhombus:
Area of Rhombus is equals to half of the product of its diagonals
To put into mathematical formula, we get:
Area of Rhombus = 1/2 (Diagonal 1 X Diagonal 2)
Or we can it as:
Area of Rhombus = 1/2 (d1 d2)
Also, note that area of rhombus is always in square units e.g. cm^{2} or m^{2} etc
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How formula for area of rhombus is obtained:
Observe the following Rhombus ABCD (as shown in Diagram 1)
Diagram 1:
AC and DB are its diagonals
O is the point of intersection of diagonals AC and DB.
And we know that diagonals of rhombus bisect each other, so we get:
AC = AO + OC and DB = DO + OB
.(Statement 1)
Rhombus ABCD comprises of Triangle ADB and Triangle BCD( as shown in diagram 2):
Diagram 2:
 Area of Rhombus ABCD = Area of Triangle ADB + Area of Triangle BCD
(Statement 2) 

Triangle ADB : Observe Triangle ADB (as shown in above diagram 1) and it has:
AO = height
DB = Base
Now apply formula of area of triangle and we get:
Area of Triangle ADB = 1/2 (Base X Height)
Area of Triangle ADB = 1/2 (DB X AO)
(Statement 3)
Triangle BCD : Observe Triangle BCD (as shown in above diagram 1) and it has:
OC = height
DB = Base
Now apply formula of area of triangle and we get:
Area of Triangle BCD = 1/2 (Base X Height)
Area of Triangle BCD = 1/2 (DB X OC)
.(Statement 4)
Area of Rhombus ABCD = Area of Triangle ADB + Area of Triangle BCD
Area of Rhombus ABCD = 1/2 (DB X AO) + 1/2 (DB X OC)
Take 1/2 DB common and we get:
= 1/2 DB (AO + OC)
As mentioned above in statement 1 (AO + OC = AC), so we get:
= 1/2 DB X AC
Since DB and AC are diagonals of Rhombus ABCD, so we get:
= 1/2 X Diagonal 1 X Diagonal 2
Or we can write it as:
= 1/2 X d1 X d2
Hence in this way formula for area of rhombus is obtained:
Area of Rhombus = 1/2 (d1 d2)
Lets use the formula to solve following example:
Example: Find area of Rhombus whose diagonals are 8 cm and 10 cm ?
Solution: As per the given question:
Diagonal 1 = 8 cm
Diagonal 2 = 10 cm
Apply formula for area of Rhombus:
Area of Rhombus = 1/2 (d1 d2)
Put given values of both the diagonals and we get:
= 1/2 (10 X 8)
= 1/2 X 80
= 40
Area of Rhombus = 40 cm^{2}


