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

From Area of Parallelogram to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Word Problems on Dividing Money | Solving Money Division Word Problems

    Feb 13, 25 10:29 AM

    Word Problems on Dividing Money
    Read the questions given in the word problems on dividing money. We need to understand the statement and divide the amount of money as ordinary numbers with two digit numbers. 1. Ron buys 15 pens for…

    Read More

  2. Addition and Subtraction of Money | Examples | Worksheet With Answers

    Feb 13, 25 09:02 AM

    Add Money Method
    In Addition and Subtraction of Money we will learn how to add money and how to subtract money.

    Read More

  3. Worksheet on Division of Money | Word Problems on Division of Money

    Feb 13, 25 03:53 AM

    Division of Money Worksheet
    Practice the questions given in the worksheet on division of money. This sheet provides different types of questions on dividing the amount of money by a number; finding the quotient

    Read More

  4. Worksheet on Multiplication of Money | Word Problems | Answers

    Feb 13, 25 03:17 AM

    Worksheet on Multiplication of Money
    Practice the questions given in the worksheet on multiplication of money. This sheet provides different types of questions on multiplying the amount of money by a number; arrange in columns the amount…

    Read More

  5. Division of Money | Worked-out Examples | Divide the Amounts of Money

    Feb 13, 25 12:16 AM

    Divide Money
    In division of money we will learn how to divide the amounts of money by a number. We carryout division with money the same way as in decimal numbers. We put decimal point in the quotient after two pl…

    Read More