Mensuration - Area of a Rectangle

Definition of Area: Area is the total amount of surface or region enclosed within a closed two-dimensional figure. Visually, if you were to shade the inside of a rectangle, the total shaded space represents its area.

Dimensions of a Rectangle: A rectangle is a four-sided polygon where opposite sides are equal and parallel. The longer side is typically designated as the Length ($l$) and the shorter side as the Breadth or Width ($b$). All four interior angles are $90^{\circ}$.

The Unit Square Concept: The area of any shape is measured by the number of unit squares that can fit inside it. For a rectangle, if you divide it into a grid of squares where each square has a side of $1\text{ cm}$, the total number of these squares is the area in $\text{sq cm}$.

Standard Units: Area is always expressed in 'square units'. Common units include square centimeters ($\text{cm}^2$), square meters ($\text{m}^2$), or square millimeters ($\text{mm}^2$). This occurs because we multiply two linear measurements together.

Relationship between Dimensions: The area is directly proportional to both length and breadth. If you visualize doubling the length while keeping the breadth constant, the total surface area of the rectangle will also double.

Unit Consistency: Before calculating the area, it is crucial to ensure that both the length and the breadth are in the same unit of measurement. For example, if length is in meters and breadth is in centimeters, convert the meters to centimeters using $1\text{ m} = 100\text{ cm}$ first.

Finding Unknown Sides: If the total area and one dimension (either length or breadth) are known, the unknown dimension can be calculated by dividing the area by the known dimension. This is the inverse operation of multiplication.