Parallelogram – Shape, Definition, Formulas, Properties, Examples

When we look around ourselves, we can see variety of shapes everywhere. The rectangular bed you are sleeping on or the circular plate you are having your food in, all are examples of shapes only. We can see tables in circle, rectangle, triangle or square form. Shapes can be of various types like 2 D shapes with only two dimensions (length and breadth) or 3 D shapes with three dimensions (length, breadth and height). Examples of 2 D shapes include circle, rectangle, square, triangle, parallelograms etc, while examples of 3 D shapes include sphere, cuboid, cube, pyramid etc. Parallelograms are 2 D shapes which are quadrilaterals that means they have four sides. They are included in polygons. If you are wondering what polygons are, then let me give you a simple idea. The polygons are 2D shapes made up of straight lines connected end-to-end to form a closed figure. Think of a polygon as a shape with many sides. Triangles, squares, rectangles all are polygons only. Now, let us circle back to the hero of today’s story: the parallelogram.

As the definition goes, “A parallelogram is a quadrilateral (four-sided polygon) in which both pairs of opposite sides are parallel and equal in length.” When we look at a parallelogram, it appears like a slanted rectangle.

Square, rectangle, and rhombus are also considered special types of parallelograms.

Rectangle is a parallelogram with right angles. Square is a parallelogram with all sides equal and right angles. Rhombus is a parallelogram with all sides equal.

Let us bullet list the properties of a parallelogram:

1. It has four sides.

2. Opposite sides of a parallelogram are parallel (hence the name), and equal.

3. In a parallelogram, opposite angles are equal.

4. A parallelogram resembles a slanted rectangle, tilted either to the left or right.

5. There are two diagonals in a parallelogram, and each diagonal divides the parallelogram into congruent triangles. Congruent triangles are triangles that are exactly the same in size and shape, that means all corresponding sides and angles are equal in them.

6. The two diagonals of a parallelogram bisect each other.

7. The adjacent angles in a parallelogram are supplementary which means their sum is equal to 180 degrees.

8. Area of a parallelogram can be calculated using its base and height or diagonals.

These are the basic properties of a parallelogram. For practical applications, we should know different specifications of a parallelogram. For instance, if we have a parallelogram shaped carpet and have to put it somewhere in our room, so we should know the area of the parallelogram, to find out the suitable place for it to fit properly. Another example is the case, when we have a parallelogram shaped wall accent and we want to border it with a LED strip light, then we must know the perimeter of the wall accent so that we can buy the exact length of the LED strip light. So, I’ll be giving you the formulas for some of the measurements of a parallelogram.

To find out the area of a parallelogram, we use the following formula:

Area (A) =Base×Height

We can also find out the area of a parallelogram using trigonometry formula.

Where area (A) = absinθ

Where a and b are adjacent sides of the parallelogram and theta is the included angle. The unit of area is metre square.

To find out the perimeter of a parallelogram we use the following formula:

Perimeter (P) = 2 (a+b)

Where a and b are the adjacent sides of the parallelogram. The standard unit for perimeter is metre. To brush up, let us solve some examples.

Example 1: Find out the area of a Parallelogram, if its base = 10 cm and height = 6 cm.

Area = Base×Height

=10×6

=60 cm2

Example 2: Find out the perimeter of a Parallelogram, if its adjacent sides are 32 m and 12 m.

Perimeter =2(a+b)

Where, a and b are adjacent sides.

Hence, P = 2(32 + 12)

= 2(44)

= 88 m

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Article Author

Srijita Banerjee

Srijita Banerjee is a freelance writer and an enthusiastic educator who loves connecting with children and helps them out to Groom Well. Srijita imbibes profound love for English and is a torch bearer. Strong believer and highly optimistic. Hardwork and dedication drives Srijita to work relentlessly towards best.

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