Area of Rhombus



Here we will learn how to find the area of rhombus.



ABCD is a rhombus whose base AB = b, DB ⊥ AC   DB = d1 AC = d2 and the altitude from C on AB is CE, i.e., h.

Area of rhombus ABCD = 2 Area of ∆ ABC
                    = 2 × 1/2 AB × CD sq units.
                    = 2 × 1/2 b × h sq. units
                    = base x height sq. units


Also, area of rhombus = 4 × area of ∆ AOB
                    = 4 × 1/2 × AO × OB sq. units
                    = 4 × 1/2 × 1/2 d2 × 1/2 d1 sq. units
                    = 4 × 1/8 d1 × d2 square units
                    = 1/2 × d1 × d2; where d1 and d2 are diagonals.
Therefore, area of rhombus = 1/2 (product of diagonals) square units

• Perimeter of rhombus = 4 × side

Worked-out examples on area of rhombus:



1. Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Solution:

ABCD is a rhombus in which AB = BC = CD = DA = 17 cm
AC = 16 cm

how to find the area of rhombus,area of rhombus

Therefore, AO = 8 cm
In ∆ AOD,
AD2 = AO2 + OD2
⇒ 172 = 82 + OD2
⇒ 289 = 64 + OD2
⇒ 225 = OD2
⇒ OD = 15

Therefore, BD = 2 OD
= 2 × 15
= 30 cm
Now, area of rhombus

= 1/2 × d1 × d2
= 1/2 × 16 × 30
= 240 cm2


2. Find the altitude of the rhombus whose area is 315 cm2 and its perimeter is 180 cm.

Solution:

Since, the perimeter of rhombus = 180 cm
Therefore, side of rhombus = P/4 = 180/4 = 45 cm
Now, area of rhombus = b × h
⇒ 315 = 45 × h
⇒ h = 315/45
⇒ h =7 cm
Therefore, altitude of the rhombus is 7 cm.


3. The floor of building consists of 2000 tiles which are rhombus shaped and each of its diagonals are 40 cm and 25 cm in length. Find the total cost of polishing the floor, if the cost per m2 is $5.

Solution:

In each rhombus, the tile length of the diagonals = 40 cm and 25 cm
Therefore, area of each tile = 1/2 × 40 × 25 = 500 cm2
Therefore, area of 2000 tiles = 2000 × 500 cm2
                    = 1000000 cm2
                    = 1000000/10000 cm2
                    = 100 m2
For 1 m2 cost of polishing = $5 = $5 × 100 = $500.

The formula of perimeter and area of rhombus are explained above with the detailed step-by-step explanation using various examples.



Mensuration

  • Area and Perimeter
  • Perimeter and Area of Rectangle
  • Perimeter and Area of Square
  • Area of the Path
  • Area and Perimeter of the Triangle
  • Area and Perimeter of the Parallelogram
  • Area and Perimeter of Rhombus
  • Area of Trapezium
  • Circumference and Area of Circle
  • Units of Area Conversion
  • Practice Test on Area and Perimeter of Rectangle
  • Practice Test on Area and Perimeter of Square

  • Mensuration - Worksheets
  • Worksheet on Area and Perimeter of Rectangles
  • Worksheet on Area and Perimeter of Squares
  • Worksheet on Area of the Path
  • Worksheet on Circumference and Area of Circle
  • Worksheet on Area and Perimeter of Triangle




  • 7th Grade Math Problems

    8th Grade Math Practice

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