# Area of a square

 Area A = a x a = a2

A side of the square = a
AB = BC = CD = DA

## Example

ABCD is a square with side a = 5 cm
Area A of the square ABCD = a x a = 5 x 5 = 25 cm²

## Calculate the area of a square

 Side a Area of the square

## Definition of a square

A square is a plane figure with four equal sides and four right (90°) angles.
A square is a quadrilateral that has 4 sides of the same length and 4 right angles.
A square is a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.

The area of a square is equal to the product of the length of one side.
Area of a square is equal to side times side. Since each side of a square is the same, it can simply be the length of one side squared.

## Properties of a square

A square has its diagonals of the same length, which intersect in their middle and are perpendicular.
A square has its opposite sides two by two parallel.
The diagonals of a square bisect each other at 90°.
The length of the diagonals of a square is equal.
The sum of all interior angles of a square is 360°.
All four sides of the square are equal to each other.
The opposite sides of a square are parallel to each other.

A square is a rectangle with four equal sides.
All squares are parallelograms, rectangles and rhombi. But not all parallelograms, rectangles and rhombi are squares.
A square has 4 sides and 4 vertices. The plural of vertex is "vertices". Vertex means a corner or a point where lines meet. "Vertex" is a synonym for a node of a graph. A vertex of a graph is one of the objects that are connected together.

## To go further

A square is a quadrilateral, as it has 4 sides and 4 angles.
A square is a rectangle. Indeed it has 4 right angles.
A square is a rhombus. Indeed it has its 4 equal sides.
Since the sides of a square are parallel, a square is a parallelogram.

## Perfect square

A perfect square is a number made by squaring a whole number. Perfect squares are numbers that are obtained by squaring a whole number or an integer. A perfect square is an integer which is the square of another integer n, that is n2. Since a negative times a negative is positive, a perfect square is always positive. Perfect squares are numbers that are squares of integers. A negative integer times a negative integer equals a positive integer.

### Examples of perfect squares

1 = 1 x 1 = 12
4 = 2 x 2 = 22
9 = 3 x 3 = 32
16 = 4 x 4 = 42
25 = 5 x 5 = 52
36 = 6 x 6 = 62
49 = 7 x 7 = 72
64 = 8 x 8 = 82
81 = 9 x 9 = 92
100 = 10 x 10 = 102
121 = 11 x 11 = 112
144 = 12 x 12 = 122
169 = 13 x 13 = 132
196 = 14 x 14 = 142
225 = 15 x 15 = 152
256 = 16 x 16 = 162
289 = 17 x 17 = 172
324 = 18 x 18 = 182
361 = 19 x 19 = 192
400 = 20 x 20 = 202
441 = 21 x 21 = 212
484 = 22 x 22 = 222
529 = 23 x 23 = 232
576 = 24 x 24 = 242
625 = 25 x 25 = 252