Area of a Rectangle Calculator
Calculate the area, perimeter, and diagonal of a rectangle from its length and width. See also Area of Parallelogram Calculator and Area of Trapezoid Calculator.
How to Calculate the Area of a Rectangle
To find the area of a rectangle, multiply its length by its width. The length is the longer side and the width is the shorter side, though the formula works regardless of which you call which. The result is in square units. You can also find the perimeter (total distance around) by adding all four sides: P = 2(l + w), and the diagonal using the Pythagorean theorem: d = √(l² + w²).
Rectangle Area Formula
Area = length × width
Perimeter = 2 × (length + width)
Diagonal = √(length² + width²)
Example
Find the area of a rectangle with length 10 and width 6:
A = length × width
A = 10 × 6
A = 60 square units
Perimeter = 2 × (10 + 6) = 32
Diagonal = √(100 + 36) = √136 ≈ 11.6619
Rectangle Area Reference Table
| Length | Width | Area | Perimeter | Diagonal |
|---|---|---|---|---|
| 2 | 1 | 2 | 6 | 2.2361 |
| 4 | 3 | 12 | 14 | 5.0000 |
| 5 | 3 | 15 | 16 | 5.8310 |
| 6 | 4 | 24 | 20 | 7.2111 |
| 8 | 5 | 40 | 26 | 9.4340 |
| 10 | 6 | 60 | 32 | 11.6619 |
| 12 | 8 | 96 | 40 | 14.4222 |
| 15 | 10 | 150 | 50 | 18.0278 |
| 20 | 12 | 240 | 64 | 23.3238 |
| 25 | 15 | 375 | 80 | 29.1548 |
| 50 | 30 | 1500 | 160 | 58.3095 |
| 100 | 50 | 5000 | 300 | 111.8034 |
Solved Examples: Area of a Rectangle
Example 1: Flooring a Living Room
A living room measures 5.5 meters long and 4 meters wide. How many square meters of laminate flooring do you need?
Length = 5.5 m, Width = 4 m
A = length × width
A = 5.5 × 4
A = 22 square meters of flooring needed
Example 2: Painting a Wall
You need to paint a wall that is 3.6 meters wide and 2.7 meters tall. If one liter covers 10 m², how much paint do you need?
Width = 3.6 m, Height = 2.7 m
A = 3.6 × 2.7
A = 9.72 square meters
Paint needed = 9.72 ÷ 10 = 0.972 liters
You need approximately 1 liter of paint
Example 3: Calculating Land Area
A rectangular plot of land measures 25 meters by 18 meters. What is the total area in square meters?
Length = 25 m, Width = 18 m
A = length × width
A = 25 × 18
A = 450 square meters (0.045 hectares)
Example 4: Fencing a Rectangular Yard
A backyard is 12 meters long and 8 meters wide. What is the area, and how much fencing do you need for the perimeter?
Length = 12 m, Width = 8 m
Area = 12 × 8 = 96 square meters
Perimeter = 2 × (12 + 8) = 2 × 20
Area = 96 m², Perimeter = 40 meters of fencing
Practice Questions
1. A bedroom is 4.2 m long and 3.5 m wide. What is its floor area?
Answer: A = 4.2 × 3.5 = 14.7 m²
2. A rectangular swimming pool is 25 m long and 10 m wide. Find the surface area of the water.
Answer: A = 25 × 10 = 250 m²
3. A poster measures 90 cm × 60 cm. What is its area in square centimeters?
Answer: A = 90 × 60 = 5,400 cm²
4. A rectangular garden has an area of 72 m² and a length of 9 m. What is its width?
Answer: Width = Area ÷ Length = 72 ÷ 9 = 8 meters
5. A tablet screen is 10.2 inches × 6.8 inches. Find the diagonal length.
Answer: d = √(10.2² + 6.8²) = √(104.04 + 46.24) = √150.28 ≈ 12.26 inches
6. A basketball court is 28 m × 15 m. How much area needs to be resurfaced?
Answer: A = 28 × 15 = 420 m²
Common Mistakes When Calculating Rectangle Area
Mixing up area and perimeter
Area = length × width (square units). Perimeter = 2(length + width) (linear units). A 10×6 rectangle has area 60 m² but perimeter 32 m.
Using inconsistent units
Both measurements must use the same unit. If length is 5 meters and width is 300 centimeters, convert first: 300 cm = 3 m, then A = 5 × 3 = 15 m².
Confusing length with diagonal
The diagonal is NOT the same as a side. For a 10×6 rectangle, the diagonal is √(100+36) ≈ 11.66, not 10. Measuring corner-to-corner gives the diagonal, not the length.
Forgetting to account for waste in real projects
When buying flooring or paint, add 5-10% extra for cuts, mistakes, and waste. A 22 m² room needs about 24 m² of material in practice.
Key Takeaways
- Rectangle area formula: A = length × width. Simple multiplication of the two sides.
- Perimeter (distance around): P = 2(l + w). Diagonal: d = √(l² + w²).
- A square is a special rectangle where l = w, so its area is simply side².
- For real-world projects (flooring, painting), always add 5-10% extra for waste and cuts.
- Rectangles with the same perimeter can have very different areas — a square always gives the maximum area for a given perimeter.
- Always ensure both dimensions use the same unit before multiplying.
Frequently Asked Questions
What is the difference between area and perimeter?
Area measures the space inside the rectangle (in square units), while perimeter measures the total distance around the outside (in linear units). Area = l × w, Perimeter = 2(l + w).
Is a square a special rectangle?
Yes. A square is a rectangle where all four sides are equal. The area formula still applies: A = side × side = side².
How do I find the diagonal of a rectangle?
Use the Pythagorean theorem: diagonal = √(length² + width²). The diagonal divides the rectangle into two right triangles.
Can I find the area if I only know the perimeter?
Not uniquely — many rectangles can share the same perimeter but have different areas. You need both length and width, or the perimeter plus one side length.