Area of a Rectangle
Reference for rectangle area A = l × w and perimeter P = 2(l+w).
Covers square as special case, diagonal, and applications for flooring and land area.
The Formula
A = l × w
The area of a rectangle is simply its length multiplied by its width.
This is one of the most commonly used formulas in everyday life.
Variables
| Symbol | Meaning |
|---|---|
| A | Area of the rectangle |
| l | Length (the longer side) |
| w | Width (the shorter side) |
Example 1
Find the area of a room that is 5 m long and 4 m wide
A = l × w = 5 × 4
A = 20 m²
Example 2
A photo is 8 inches by 10 inches. What is its area?
A = l × w = 10 × 8
A = 80 square inches
When to Use It
Use the area of a rectangle formula when:
- Calculating floor space, wall area, or land size
- Figuring out how much paint, carpet, or tile you need
- Determining the size of screens, photos, or paper
- Working with any four-sided shape with all right angles
Key Notes
- A square is a special rectangle where l = w, so its area simplifies to A = s²
- The diagonal of a rectangle is d = √(l² + w²) — a common mistake is adding l + w instead
- Units must be consistent — mixing feet and inches gives wrong results; convert everything to one unit before multiplying
- For irregular rooms, split the floor plan into separate rectangles, calculate each area, then add them together
Key Notes
- Formulas: Area = l × w; Perimeter = 2(l + w): Area measures the space inside; perimeter measures the total boundary length. Both require the same two measurements but answer completely different questions — a large room and a thin hallway can have the same perimeter but very different areas.
- Diagonal: d = √(l² + w²): Derived from the Pythagorean theorem applied to the right triangle formed by two sides and the diagonal. The diagonal of a rectangle with sides 3 and 4 is exactly 5 (a 3-4-5 right triangle).
- Isoperimetric property — the square maximizes area: Of all rectangles with a fixed perimeter P, the square (l = w = P/4) encloses the maximum area P²/16. This is why square rooms use floor area most efficiently for a given amount of wall material.
- Scaling behavior: If both dimensions are scaled by factor k, area scales by k² and perimeter scales by k. Doubling all dimensions quadruples the area but only doubles the perimeter — important in architecture and manufacturing.
- Applications: Rectangle area calculations are fundamental in architecture (floor plans, window sizing), agriculture (field area), manufacturing (material cutting), and digital imaging (pixel count = width × height in pixels).