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Home >> Rhombus >> Area of Rhombus >>

## Area of Rhombus

 Area of Rhombus Difference & Similarity between Rhombus & Rectangle Difference & Similarity between Rhombus & Square Difference & Similarity between Rhombus & Parallelogram Construction of Rhombus with Compass

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. cm2 or m2 etc..

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)

Lets 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 cm2