1. Area of a Square
A square is a special quadrilateral where all four sides are equal and every angle is \(90^\circ\). Because all sides have the same length, it is one of the simplest shapes to calculate area for.
The area of a square tells us how much space is enclosed inside the shape. Area is always measured in square units like \(\text{cm}^2\), \(\text{m}^2\), or \(\text{km}^2\).
1.1. Definition of Area
The area of a square is defined as the region covered when the side length is multiplied by itself. Since all sides are equal, the idea becomes very straightforward: "side × side".
2. Area Formula
If each side of the square has length \(a\), then its area is obtained by multiplying the side by itself:
\( A = a^2 \)
2.1. Why the Formula Works
Picture the inside of a square as being filled with tiny 1 × 1 square units. Along one side, you can fit exactly \(a\) such units. The same is true for the adjacent side.
So the total number of 1 × 1 squares that fill the entire square is:
\( a \times a = a^2 \)
This is why the area of a square grows quickly as the side increases.
3. Examples
These simple examples show how to apply the formula.
3.1. Example 1
A square has side length \(a = 9\,\text{cm}\). Its area is:
\( A = a^2 = 9^2 = 81\,\text{cm}^2 \)
3.2. Example 2
A garden is in the shape of a square with each side \(a = 20\,\text{m}\). The total area covered is:
\( A = 20^2 = 400\,\text{m}^2 \)