# Parallelogram(KS2, Year 6)

## The Lesson

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:

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:

In this formula, b is the length of the base and h is the height of the parallelogram.

## 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?

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