Parallelogram Formula: Theorems and Formulas

A parallelogram is a two-dimensional shape. It has four arms, of which two pairs of opposite arms are parallel. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure, while the sum of the adjacent angles of a parallelogram is equal to 180 degrees. A quadrilateral is a closed geometric shape with 4 vertices, 4 sides and so 4 angles that are located on the same plane. For a quadrilateral, the sum of the interior angles is 360 degrees. A quadrilateral is a type of polygon. There are different types of quadrangles embracing Trapezoids, parallelograms, and kites.

Key Takeaways: Parallelogram, quadrilateral, parallel, Area, Perimeter, dimensional, congruent, parallelepiped

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What is Parallelogram?

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A parallelogram is a quadrilateral with two parallel and equal sides. A quadrilateral is called a parallelogram if two pairs of opposite sides of a quadrilateral are equal then it is a parallelogram. If two opposite sides of a quadrilateral are parallel and equal, then this quadrilateral is a parallelogram. If inside a quadrilateral, the corners bisect each other, then this quadrilateral is a parallelogram.

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Theorem of Parallelogram

Following are the Theorems of Parallelogram:

Theorem 1: Parallelograms on the same base and between the same parallel sides are equal in area.

Theorem 2: The area of a parallelogram is the product of its base and the corresponding altitude.

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What is Parallelogram Formula?

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A geometric shape with two opposite arms and opposite angles equal is defined as a parallelogram. If the image is two-dimensional, it is called parallelogram, and if the image is three-dimensional, it is called parallelepiped.

The formula for the area of a parallelogram is, Area = b × h

The formula for the perimeter of a parallelogram is, = 2 (a + b)

Where the base of a parallelogram is b and the height of that parallelogram is h and a is the side adjacent to the base.

Perimeter of a Parallelogram Formula

The circumference of a parallelogram is the total distance of the boundary of a parallelogram. To determine the circumference of a parallelogram, one needs to know its length and width. Let the arms of the parallelogram be a and b. Keeping in mind the characteristics of a parallelogram, that is, the opposite arms are parallel and consistent. The perimeter of a parallelogram is as given below:

• Perimeter = a + b + c + d (when a, b, c, d are representing 4 sides of a parallelogram)
• Since, side AB = CD = b, side BC = AD = a; Perimeter of a parallelogram = 2 (a + b)

Area of a Parallelogram Formula

The number of square units inside the polygon is the area of a parallelogram. The area of a parallelogram is the area or surface occupied by a two-dimensional plane. The area of a parallelogram can be determined by multiplying the base and the height. To find the area of a parallelogram, the base and height must be perpendicular.

Area of Parallelogram Formula Using Height and Base

• Area of parallelogram formula = Base × Height
• Area of Parallelogram = b × h

Area of a Parallelogram Formula Without Height

• In case of height of the parallelogram is not given, trigonometry can be used to find the area.
• Area of parallelogram formula = a b sin (x) = b a sin (x)

Area of a Parallelogram Using Diagonals

Also, the area of any parallelogram can be calculated using its diagonal lengths of it. Let’s assume, the diagonals d1 and d2 intersect each other at an angle x, then the area of the parallelogram is given by: 

• Area of parallelogram formula = ½ × d1 × d2sin (x)

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Points to Remember

Following are some important points:

• All parallelograms are quadrilaterals.
• All quadrilaterals are not parallelograms.
• All Squares and Rectangle will have the properties of parallelograms while all the parallelograms may not be squares or rectangles.
• The only example of a regular quadrilateral is square. 
• The volume of a parallelogram cannot be determined as a parallelogram is a two-dimensional shape.
• Not all parallelograms and not all quadrilaterals are parallel.

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