Rectangle Area — Counting the Grid

Plain English first

A rectangle is the simplest area to measure because you can just count.

Lay a grid of unit squares inside it. Count the columns. Count the rows. Multiply. That number is the area — the total count of unit squares that fit inside without overlapping or leaving gaps.

The formula A = l×w is not a rule someone made up. It's a shortcut for that counting. 4 columns of 5 squares each = 20 squares. Length times width equals total.

Every other area formula on this page is built on top of this one.

Standard math notation

A = l × w

Where:
  A = area (total unit squares inside the rectangle)
  l = length (number of columns of squares)
  w = width  (number of rows of squares)

Units: if l and w are in meters, A is in square meters (m²)

Verbose Python with descriptive names

def compute_rectangle_area(
    length_of_rectangle,
    width_of_rectangle
):
    """
    Area is the count of unit squares that tile the interior exactly.
    Columns of squares times rows of squares equals total squares inside.
    """
    number_of_columns_of_squares = length_of_rectangle
    number_of_rows_of_squares    = width_of_rectangle
    total_unit_squares_inside    = number_of_columns_of_squares * number_of_rows_of_squares
    return total_unit_squares_inside

area = compute_rectangle_area(
    length_of_rectangle=4,
    width_of_rectangle=5
)
print(f"Area: {area} square units")  # 20

# A square is a special rectangle where length equals width
def compute_square_area(side_length):
    return compute_rectangle_area(side_length, side_length)

print(compute_square_area(side_length=3))  # 9

Why this is the foundation

Every 2D area formula is either a rectangle or a transformation of one:

See also

• Triangle Area — Half a Rectangle
• Circle Area — Why πr²?
• What Is a Number?
• Base 10 and Place Value
• Math Foundations — Visual Table of Contents