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    = 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.

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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