# Why is the area of a square a2?

The area of a square being equal to side squared can be better understood by breaking down the concept of area and the properties of a square.

Firstly, let’s talk about what area is. Area is a measure of the amount of space inside a 2D figure. It is calculated by multiplying the length and width of the figure. In the case of a square, the length and width are the same because all the sides of a square are equal.

Now, let’s consider the properties of a square. A square is a special type of quadrilateral where all four sides are equal in length and all four angles are right angles. These equal sides make a square a regular polygon.

When we calculate the area of a square, we can think of it as dividing the square into smaller square units. Each side of the square can be seen as a unit of length, and by multiplying the length by the width (which is also the length in this case), we are essentially multiplying the side length by itself.

For example, if we have a square with a side length of 5 units, the area would be calculated as 5 units × 5 units, which equals 25 square units. In this case, the units of measurement (such as centimeters or inches) are squared because we are multiplying the side length by itself.

This concept can be visualized by drawing a square on graph paper and counting the number of smaller squares that fit inside it. Each smaller square represents a unit of area, and the total number of smaller squares gives us the total area of the square.

To further illustrate this concept, let’s consider a real-life scenario. Imagine you have a square tile with a side length of 1 foot. If you wanted to cover a floor with these tiles, you would need to know the total area of the floor to determine how many tiles you would need. By calculating the area of the square tile (1 foot × 1 foot = 1 square foot), you can easily determine the number of tiles needed by dividing the total area of the floor by the area of each tile.

The area of a square is side squared because all the sides are equal, and when we calculate the area, we are essentially multiplying the side length by itself. This concept is applicable to various real-life situations and allows us to determine the amount of space inside a square or the number of square units needed to cover a given area.