## The Lesson

A square is a four sided shape with four equal sides and four right angles. ## Dictionary Definition

The Oxford English Dictionary defines a rectangle as "a plane rectilinear and rectangular figure with four equal sides."
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## Properties of Squares

• All sides of a square are of equal length. • All angles in a square are right angles. • Opposite sides of a square are parallel. • All angles of a square add up to 360°. • The diagonals of a square bisect each other at right angles. The diagonals cross each other half-way along their lengths and are perpendicular to each other. ## The Perimeter of a Square

The perimeter of a square is given by the formula: In this formula, a is the length of the side of the square.

## The Area of a Square

The area of a square is given by the formula: In this formula, a is the length of the side of the square.

## A Square is a Polygon

A square is a type of polygon. A polygon is a 2-dimensional shape with straight sides. A square is a regular polygon. Regular polygons have the same length sides and the same angles.

## A Square Is a Quadrilateral

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

## Square Numbers...

A square number is a number multiplied by itself.
12 = 1 × 1 = 1 22 = 2 × 2 = 4 32 = 3 × 3 = 9
The squares go 1, 4, 9... A square with side length 1 has an area of 1. A square with side length 2 has an area of 4. A square with side length 3 has an area of 9. The areas go 1, 4, 9... The square of a number and the area of a square with side lengths of that number are the same.

## ...and Square Roots

A square root is the inverse of a square number. If a number represented the area of a square, then the square root represents the length of the side of that square.