# Area of a Square

How to find the area of a square: formula, examples, and their solutions.

## Definition

A square is a parallelogram

that have congruent sides and congruent angles.

It's a rectangle (angles) and a rhombus (sides).

So it has both properties.

## Formula

*A* = *a*^{2}*A*: area of a square*a*: side

## Example 1

*a* = 4*A* = 4^{2}

## Example 2

The square is a rhombus.

So the diagonals perpendicularly bisect each other.

So the brown segments are 3.

Diagonals of a rhombus

The bottom triangle is an isosceles right triangle.

So it's similar to a 45-45-90 triangle.

Draw a 45-45-90 triangle next to the given square.

The left triangle is × 3 bigger.

So the left triangle's hypotenuse is 3⋅√2.

*a* = 3√2*A* = (3√2)^{2}

There's another way to solve this example.

The square is a rectangle.

So the blue segments formed by the diagonals

are all congruent: 3.

Diagonals of a rectangle

The square is also a rhombus.

And the diagonals are 6 and 6.

So the area of the rhombus is (1/2)⋅6⋅6.