The area of a rectangle is calculated by multiplying its length by its width. If \( a \) represents the length of the rectangle and \( b \) denotes its width, then the formula for the area of the rectangle would be: \[ \text{Area} = a \times b \] This formula is derived from the basic concept that the area of a rectangle is found by multiplying the length (one side) by the width (the adjacent side). Each side of the rectangle, when multiplied together, gives the total area enclosed by the shape.

Geometrically, a rectangle is a quadrilateral with four right angles and opposite sides that are equal in length. The area represents the total space contained within these four sides. Therefore, the product of the length and width provides the area of the rectangle.

Visually, if you consider a rectangle where \( a \) is the length and \( b \) is the width, the area calculation (length × width) covers the entire surface within the rectangle's boundaries.

Hence, the formula \( a \times b \) accurately determines the area of a rectangle, providing a simple and direct method to find the total space enclosed within its four sides.