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Parallelogram

(KS2, Year 6)

A paralleogram is a four sided shape with opposite sides parallel and equal in length.

Dictionary Definition

The Oxford English Dictionary defines a parallelogram as "a four-sided plane rectilinear figure whose opposite sides are parallel; especially one whose sides do not intersect at right angles."

Properties of Parallelograms

Opposite sides of a parallelogram are parallel.
Opposite sides of a parallelogram are of equal length.
Opposite angles of a parallelogram are equal.
Adjacent angles of a parallelogram add up to 180°. They are supplementary angles.
All angles of a parallelogram add up to 360°.
The diagonals of a parallelogram bisect each other. The diagonals cross each other half-way along their lengths.

The Perimeter of a Parallelogram

The perimeter of a parallelogram is given by the formula:

perimeter equals 2 )b plus s)

In this formula, b is the length of the base and s is the length of the side of the parallelogram.

The Area of a Parallelogram

The area of a parallelogram is given by the formula:

area of a parallelogram equals b h

In this formula, b is the length of the base and h is the height of the parallelogram.
how to find the area of a parallelogram

Interactive Widget

Here is an interactive widget to help you learn about parallelograms.

What's in a Name?

Parallelogram comes from the Greek word "parallelogrammon" meaning 'parallel sides'.

A Parallelogram is a Polygon

A parallelogram is a type of polygon. A polygon is a 2-dimensional shape with straight sides. A parallelogram is an irregular polygon. Irregular polygons have different length sides and different angles.

A Parallelogram Is a Quadrilateral

A parallelogram is a quadrilateral. A quadrilateral is a four-sided polygon. Squares, rectangles and trapezoids are also quadrilaterals.

Interior Angles of a Parallelogram

A parallelogram is a four-sided polygon. The sum of the interior angles of an n-sided polygon is is:

(n − 2) × 180°

This means the interior angles of a quadrilateral (where n = 4) add up to:

(4 − 2) × 180° = 360°

This is the case for all quadrilaterals, such as squares, rectangles and trapezoids.

Areas of Parallograms and Rectangles

The formula for the area of a parallelogram is the same as for the area of a rectangle. Can you see why from the image below?

area of a parallelogram equal to area of a rectangle of same base and height