# Area of a Square Using its Side

The area of a square is determined by multiplying one side by itself. Since all sides of a square are equal in length, if we represent the length of one side as \(s\), the area can be expressed as \(s \times s\), which equals \(s^2\).

**Example 1:** Find the area of the square below that is drawn on a grid.

Given the square is drawn on a grid, we can easily determine the length of its side by simply counting the number of units. Counting the measure of one side along the horizontal, we find that there are \(5\) units. The number of units along the vertical is also \(5\) units.

Since the side length of the given square is \(5\) units, we can substitute that value into the formula and then simplify.

$$\eqalign{

A &= {s^2} \cr

& = {\left( 5 \right)^2} \cr

& = 25\,\,\cr} $$

Therefore, the area of the square is \(25\) square units.

**Example 2:** A square has an area of \(49 \ \text{ft}^2\). What is the length of each side?

To determine the length of the side of a square with an area of \(49\) square feet, we need to find the square root of the area.

$$\eqalign{

A &= {s^2} \cr

49 &= {s^2} \cr

\sqrt {49} &= s \cr

7 &= s \cr} $$

Therefore, the side length of the square is \(7\) \(\text{ft}\).