Mensuration - Area of a Square

A square is a flat geometric shape with four equal sides and four right angles ($90^{\circ}$). In a visual diagram, this is represented by a closed figure where all four boundary lines are of the same length, often indicated by small hash marks on each side, and each corner contains a small square symbol to show the right angle.

The Area of a square refers to the amount of flat surface covered by the shape. If you were to paint the inside of a square drawn on the ground, the total amount of paint used to cover the surface would correspond to its area. It is the 'space' within the perimeter.

To find the area of a square, we multiply the length of one side by itself. Since all sides are equal in length, the calculation involves taking the measure of one side and squaring it. This can be visualized as creating a grid of equal rows and columns inside the square.

The unit of area is always expressed as 'square units'. For example, if the side of a square is measured in centimeters ($cm$), the area is measured in square centimeters ($cm^2$). This represents how many small $1 \times 1$ unit squares can perfectly fit inside the larger square.

A helpful way to visualize area is through a grid system. If a square has a side length of $3$ units, you can draw $3$ rows and $3$ columns inside it. Counting the resulting small boxes gives you $3 \times 3 = 9$ units of area.

It is crucial to distinguish between Perimeter and Area. While perimeter is the distance around the outer edge (like a fence), area is the total space occupied inside those edges (like the grass in a garden).