What is a Parallelogram? Explained

ElevatEd
Math
June 18, 2025

Consider a shape that is close to a rectangle tilted to one side, or a square elongated into a diamond. That is a parallelogram - a wonderful and fascinating geometric shape! Whether you are calculating its area, studying its properties, or discovering it in daily life, parallelograms are everywhere around us. For parents and students of 1-12, discovering what a parallelogram is a polygon and how to find parallelogram real-life examples can make geometry more fascinating and relevant.

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Let's discover the world of parallelograms and learn its secrets in this article.

What is a Parallelogram?

A parallelogram is a two-dimensional quadrilateral shape with four sides where the two pairs of opposite sides are equal in length and parallel. It is a polygon with special symmetry that makes it different from other polygons.

Key Properties of a Parallelogram

They both (both dimensions) have the same length and are parallel.
Opposite angles are congruent.
Supplementary angles are adjacent angles (their total is 180°).
Diagonals bisect each other equally in the middle.

Is a Parallelogram a Polygon?

Yes! A parallelogram is a polygon because it is a closed figure with straight edges.

Types of Parallelograms

Parallelograms exist in various shapes, each with a special characteristic:

Type	Description	Example
Rectangle	All angles are 90°, and opposite sides are equal and parallel.	A standard book cover.
Square	All sides are equal, and all angles are 90°.	A chessboard square.
Rhombus	All sides are equal, but angles aren’t necessarily 90°.	A kite-shaped diamond pattern.
Rhomboid	Opposite sides are parallel, but angles and side lengths vary.	A leaning windowpane design.

Properties of Parallelograms

Knowing the properties of parallelograms allows them to be easily identified:

Property	Explanation
Opposite Sides	Equal in length and parallel to each other.
Opposite Angles	Equal in measure (e.g., ∠A = ∠C).
Adjacent Angles	Supplementary (e.g., ∠A + ∠B = 180°).
Diagonals	Bisect each other at right angles or midpoints.
Sum of Interior Angles	Always equals 360°.

Formulas for Parallelograms

1. Area

The formula for the area of a parallelogram is:

Area = Base × Height

Example: When base is 8 cm and height is 5 cm:

Area = 8 × 5 = 40 cm²

2. Perimeter

The perimeter is the distance around the entire parallelogram:

Perimeter = 2 (Base + Side)

Example: When the base is 10 cm and the side is 6 cm:

Perimeter = 2 (10 + 6) = 32 cm

Parallelogram Real-Life Examples

Parallelograms don't exist only as theoretical shapes - they're everywhere! Let's look at some examples:

Architecture: The inclined walls of some buildings are similar to parallelograms.
Engineering: Bridges usually use parallelogram-shaped trusses as supports.
Art and Design: Parallelograms often appear in designs in tiles or fabrics.
Equipment: Pantographs (image scaling devices) are parallelogram mechanics based.

Fun Fact: Did You Know?

The term "parallelogram" is derived from the Greek term parallēlógrammon, meaning "a figure composed of parallel lines." It's one of the earliest geometric shapes that mathematicians have studied!

How Can 98thPercentile's Math Course Help Students?

At 98thPercentile, we recognise geometry can be quite daunting when you don't know where to turn. Our mathematics program breaks down complicated topics like parallelograms into easy-to-understand lessons designed for 1-12 students.

Parallelograms are not only figures, they are the foundation of geometry that are used in art, architecture, engineering, and so much more! Studying their properties, formulas, and uses in everyday life enables students to think on higher levels and see how mathematics is used in their everyday lives. For those parents looking for alternatives to further develop their child's math studies, consider having them take 98thPercentile's math courses - where parallelograms and other math concepts are easily grasped through engaging lessons!

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