Area of Parallelogram



Here we will discuss about how to find the area of a parallelogram. To calculate area of parallelogram we need to remember the formula and solve step-by-step.



ABCD is a parallelogram with base (b) and altitude (h).

area of parallelogram,perimeter of parallelogram



Area of parallelogram = 2 × Area of ∆ABC

= 2 × 1/2 × base × height sq. units
= 2 × 1/2 × AB × CE sq. units
= b × h sq. units
= base × height sq. units
Perimeter of parallelogram = 2(AB + BC)

= 2 × (Sum of adjacent sides)


Worked-out examples on area of parallelograms:

1. The base of the parallelogram is thrice its height. If the area is 192 cm2, find the base and height.

Solution:

Let the height of the parallelogram = x cm
then the base of the parallelogram = 3x cm
Area of the parallelogram = 192 cm2

Area of parallelogram = base × height
192 = 3x × x
⇒ 3x2 = 192
⇒ x2 = 64
⇒ x = 8
Therefore, 3x = 3 × 8 = 24
Therefore, Base of the parallelogram is 24 cm and height is 8 cm.


2. A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.

Solution:

Adjacent sides of parallelogram = 2 cm and 9 cm
Distance between shorter sides = 8 cm
Area of parallelogram = b × h
= 9 × 8 cm2 = 72 cm2

Again, area of parallelogram = b × h
⇒ 72 = 12 × h
⇒ h = 72/12
⇒ h = 6 cm
Therefore, the distance between its longer side = 6 cm.


3. ABCD is a parallelogram in which AB = 20 cm, BC = 13 cm, AC = 21 cm. Find the area of parallelogram ABCD.

area of parallelogram,perimeter of parallelogram



Solution:

Area of parallelogram ABCD = 2 area of ∆ABC
In ∆ ABC,
AB = 20 cm BC = 13 cm AC = 21 cm
So, s = (20 + 15 + 21)/2
= 54/2
= 27

Therefore, area of ∆ABC = √(27 (27 - 20) (27 - 13) (27 - 21))
= √(27 × 7 × 14 × 6)
= √(3 × 3 × 3 × 7 × 2 × 7 × 2 × 3)
= 2 × 3 × 3 × 7
= 126 cm2

Area of parallelogram ABCD = 2 area of ∆ABC
= 2 × 126 cm2
= 252 cm2

The detailed explanations on the formula of perimeter and area of parallelogram are explained above with the step-by-step solution.



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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