Area and Perimeter - Area of Rectangles and Squares

Definition of Area: Area is the total amount of surface or region covered by a closed 2D shape. Imagine covering a floor with square tiles; the total number of tiles used represents the area of that floor.

Units of Area: Area is always measured in square units. Visually, we represent this as small squares of $1\ unit \times 1\ unit$. Common units include square centimeters ($cm^2$), square meters ($m^2$), and square kilometers ($km^2$).

Understanding the Rectangle: A rectangle is a quadrilateral with opposite sides equal and four right angles ($90^\circ$). The longer side is called the length ($l$) and the shorter side is called the breadth or width ($b$).

Understanding the Square: A square is a special rectangle where all four sides are equal in length. If you look at a square grid, it has the same number of rows as it has columns.

Area Calculation for Rectangles: To find the area of a rectangle, you multiply its length by its breadth. This is similar to counting the total number of unit squares in an array with $l$ columns and $b$ rows.

Area Calculation for Squares: Since all sides of a square are equal, the area is found by multiplying the side by itself. Visually, a square with side $s$ forms a grid of $s \times s$ small squares.

Finding Dimensions from Area: If the area and one dimension (length or breadth) of a rectangle are known, the missing dimension can be found by dividing the area by the known dimension.

Comparing Area and Perimeter: While perimeter is the distance around the outside 'fence' of a shape, area is the 'grass' or space inside that fence. Two shapes can have the same perimeter but different areas.