# Rectangle Area — Counting the Grid
> **Animation coming** — full Sora 2 prompt below. Video will replace this placeholder.
## 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
```python
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
```
---
## Sora 2 video prompt
```
8-second animation. Split screen. Left: a white rectangle labeled l=4 and w=5.
Grid lines appear and 20 unit squares fill in column by column, each glowing
warm gold as it fills. A counter shows the total building to 20. Right: the
formula A = l×w animates — 4 columns × 5 rows = 20 — with grid squares
matching the left side. Both resolve simultaneously. Clean white background,
warm earth tones, educational textbook style.
```
---
## Why this is the foundation
Every 2D area formula is either a rectangle or a transformation of one:
| Shape | Trick | Formula |
|-------|-------|---------|
| Parallelogram | Slide the end off and reattach — still same grid | A = bh |
| Triangle | Cut a rectangle diagonally — exactly half | A = ½bh |
| Trapezoid | Average of two bases times height | A = ½h(b₁+b₂) |
| Circle | Grid squares fill the interior — π corrects for curved edges | A = πr² |
---
## See also
- [Triangle Area — Half a Rectangle](/articles/triangle-area)
- [Circle Area — Why πr²?](/articles/circle-area)
- [What Is a Number?](/articles/8510b9a8-a3ad-4790-a928-b2360ac8679e)
- [Base 10 and Place Value](/articles/c92b632e-5a6d-4e17-b5fa-ec41f0db4d3f)
- [Math Foundations — Visual Table of Contents](/articles/d404884f-54fc-4289-b3f1-baaad2bec6b2)