Formula

Area of a rectangle

Also written: length times width · area of a square · rectangle area formula

A = l \times w

The area of a rectangle is its length times its width. A square is the special case where they are equal, giving A = s².

What each part means

$l$: the length, one side of the rectangle
$w$: the width, the side next to it

When to use it

You need the space inside a rectangle or square — floor area, wall area, a field, a screen. Also the first step for the volume of a box.

It counts squares

The formula is not a rule to accept — it is what counting unit squares turns into. A rectangle $8$ by $5$ holds $5$ rows of $8$ squares, and multiplying is how you count equal rows.

5 \times 8 = 40 \text{ square units}

Why the units are squared

Each tile is one centimetre wide and one centimetre tall — one square centimetre. A count of them is written cm².

The exponent records how many lengths were multiplied, which is the fastest check on any measurement answer:

Multiplied	Quantity	Units
one	perimeter	cm
two	area	cm²
three	volume	cm³

A number reached by adding lengths cannot carry square units, so “perimeter = 24 cm²” is impossible on inspection.

A square is the same formula

A = s \times s = s^2

This is where the word “squared” for a second power comes from: $s^2$ is the area of a square with side $s$ .

Rearranged

l = \frac{A}{w} \qquad w = \frac{A}{l}

A rectangle of area $40$ cm² with a length of $8$ cm has a width of $5$ cm.

Awkward shapes

Areas add. An L-shape splits into rectangles, and its area is the sum of the pieces — cut it wherever is convenient, so long as the pieces do not overlap.

(6 \times 4) + (3 \times 2) = 30

Area is not perimeter

	Measures	Units
area	space inside	cm²
perimeter	distance around	cm

Two rectangles can share an area and have very different perimeters: $6 \times 6$ and $2 \times 18$ both cover $36$ cm², but need $24$ cm and $40$ cm of fence. See area of a rectangle.

Lessons that teach this

Area of a Rectangle: Length Times Width
Why the area of a rectangle is length times width, how to find a missing side, why area uses square units, and how to handle L-shaped figures.
Volume of a Rectangular Prism: Length × Width × Height
Why the volume of a box is length times width times height, why the units are cubed, and how the base-times-height form works for any prism.
Perimeter: The Distance Around a Shape
What perimeter means, how to find it for any shape by adding the sides, the rectangle shortcut, and how to work backwards from a known perimeter.