Area Of A Parallelogram, Definition, Formula, Examples

Safalta expert Published by: Yashaswi More Updated Fri, 30 Sep 2022 10:04 AM IST

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Read this article on how to find the area of a parallelogram- definition, formula and examples here at Safalta.com.

The parallelogram is one of many geometric shapes. It is a quadrilateral with equal and opposite parallel sides. Understanding the area and perimeter of these figures is critical for anyone studying geometry. The area of a parallelogram is the space it encloses. You may calculate it by multiplying the length by the height. All pupils can find information regarding the area of a parallelogram in this article. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that students have conceptual clarity in all the subjects and are able to score their maximum in the exams.

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Table of Content 

1. What is the Area of Parallelogram?
2. Area of Parallelogram Formula
3. Calculation of the Area of Parallelogram
           i) Area of Parallelogram Using Sides
          ii) Area of Parallelogram Without Height
          iii) Area of Parallelogram Using Diagonals

 


What is the Area of Parallelogram?

The area of a parallelogram is the region that it circumscribes in a given two-dimensional space. A parallelogram is a specific sort of quadrilateral having four parallel sides.

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A parallelogram has opposed sides that are the same length and opposite angles that are the same size. Because the properties of a rectangle and a parallelogram are equivalent, the area of a rectangle equals the area of a parallelogram.

Area of Parallelogram Formula

To find the area of the parallelogram, multiply the base of the perpendicular by its height. It should be noted that the base and the height of the parallelogram are perpendicular to each other, whereas the lateral side of the parallelogram is not perpendicular to the base. Thus, a dotted line is drawn to represent the height.

Therefore,

Area = b × h Square units

Where “b” is the base and “h” is the height of the parallelogram.

Let us learn the derivation of area of a parallelogram, in the next section.

 

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How to Calculate the Area of Parallelogram?

The parallelogram area can be calculated, using its base and height.

Apart from it, the area of a parallelogram can also be evaluated, if its two diagonals are known along with any of their intersecting angles, or if the length of the parallel sides is known, along with any of the angles between the sides. Hence, there are three method to derive the area of parallelogram:

  • When base and height of parallelogram are given
  • When height is not given
  • When diagonals are given
 

Area of Parallelogram Using Sides

Suppose a and b are the set of parallel sides of a parallelogram and h is the height, then based on the length of sides and height of it, the formula for its area is given by:

Area = Base × Height

A = b × h     [sq.unit]
 

Example: If the base of a parallelogram is equal to 5 cm and the height is 3 cm, then find its area.

Solution: Given, length of base=5 cm and height = 3 cm

As per the formula, Area = 5 × 3 = 15 sq.cm


 

Area of Parallelogram Without Height

If the height of the parallelogram is unknown to us, then we can use the trigonometry concept here to find its area.

Area = ab sin (x)

Where a and b are the length of parallel sides and x is the angle between the sides of the parallelogram.
 

Example: The angle between any two sides of a parallelogram is 90 degrees. If the length of the two parallel sides is 3 cm and 4 cm respectively, then find the area.

Solution: Let a = 3 cm and b=4 cm

x = 90 degrees

Area = ab sin (x)

A = 3 × 4 sin (90)

A = 12 sin 90

A = 12 × 1 = 12 sq.cm.

Note: If the angle between the sides of a parallelogram is 90 degrees, then it is a rectangle.


 

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Area of Parallelogram Using Diagonals

The area of any parallelogram can also be calculated using its diagonal lengths. As we know, there are two diagonals for a parallelogram, which intersects each other. Suppose, the diagonals intersect each other at an angle y, then the area of the parallelogram is given by:

Area = ½ × d1 × d2 sin (y)


 

Check the table below to get summarised formulas of an area of a parallelogram.

All Formulas to Calculate Area of a Parallelogram
Using Base and Height A = b × h
Using Trigonometry A = ab sin (x)
Using Diagonals A = ½ × d1 × d2 sin (y)

Where,

  • b = base of the parallelogram (AB)
  • h = height of the parallelogram
  • a = side of the parallelogram (AD)
  • x = any angle between the sides of the parallelogram (∠DAB or ∠ADC)
  • d1 = diagonal of the parallelogram (p)
  • d2 = diagonal of the parallelogram (q)
  • y = any angle between at the intersection point of the diagonals (∠DOA or ∠DOC)

 

What is a Parallelogram?

A parallelogram is a geometrical figure that has four sides formed by two pairs of parallel lines. In a parallelogram, the opposite sides are equal in length, and opposite angles are equal in measure.

What is the Area of a Parallelogram?

The area of any parallelogram can be calculated using the following formula:

Area = base × height

It should be noted that the base and height of a parallelogram must be perpendicular.

What is the Perimeter of a Parallelogram?

To find the perimeter of a parallelogram, add all the sides together. The following formula gives the perimeter of any parallelogram:

Perimeter = 2 (a + b)

What is the Area of a Parallelogram whose height is 5 cm and base is 4 cm?

The area of a perpendicular with height 5 cm and base 4 cm will be;

A = b × h

Or, A = 4 × 5 = 20 cm square.

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