Area of a Rectangle- Formula and Examples
What Is a Rectangle?
A rectangle is a four-sided shape where opposite sides are equal in length and all angles are 90 degrees. That's it. No tricks, no curves—just straight lines and right angles.
You've seen them everywhere. Doors. Phone screens. Basketball courts. Book covers. They're the most common shape you'll encounter in everyday geometry.
The Area Formula
The formula for finding the area of a rectangle is:
Area = Length × Width
Sometimes written as: A = l × w
Both numbers must be in the same units (inches to inches, meters to meters, etc.). Mixing units gives you garbage results. Don't do it.
How to Calculate the Area
Here's the process:
- Measure the length of one side
- Measure the width of the adjacent side
- Multiply those two numbers together
- The result is your area
That's it. Three steps. No calculus, no advanced theory.
Examples
Example 1: Basic Calculation
A rectangle has a length of 8 cm and a width of 5 cm.
A = 8 cm × 5 cm = 40 cm²
The area is 40 square centimeters.
Example 2: Larger Numbers
A room measures 15 feet by 12 feet.
A = 15 ft × 12 ft = 180 ft²
The room covers 180 square feet. Useful if you're buying flooring.
Example 3: Real-World Application
You want to paint a wall. The wall is 20 feet wide and 10 feet tall.
A = 20 ft × 10 ft = 200 ft²
One gallon of paint typically covers about 350 square feet. So you'd have plenty left over for touch-ups. 👍
Units of Measurement
Area is always expressed in square units. The unit depends on what you're measuring:
- cm² — centimeters squared (small objects, homework problems)
- m² — meters squared (rooms, apartments)
- ft² — feet squared (real estate, construction)
- in² — inches squared (small items, crafts)
- km² — kilometers squared (land, geography)
Quick Reference: Area Formulas for Common Shapes
| Shape | Formula |
|---|---|
| Rectangle | Length × Width |
| Square | Side × Side (or Side²) |
| Triangle | ½ × Base × Height |
| Circle | π × Radius² |
| Parallelogram | Base × Height |
Notice the rectangle formula is the simplest of the bunch. That's one reason it's taught first.
Common Mistakes to Avoid
- Using the wrong sides: Make sure you're multiplying the two adjacent sides, not opposite sides twice. Length and width are perpendicular, not parallel.
- Forgetting to square the unit: Your answer isn't "40 cm"—it's "40 cm²". That little 2 matters.
- Mixed units: If one side is in inches and the other is in feet, convert first. Otherwise your answer is wrong.
- Confusing perimeter with area: Perimeter is the distance around the shape (2L + 2W). Area is the space inside. Different calculations entirely.
Finding Missing Dimensions
What if you know the area and one side, but need the other side?
Width = Area ÷ Length
Or:
Length = Area ÷ Width
Example: You need a rectangle with an area of 48 square inches and one side is 8 inches.
Width = 48 ÷ 8 = 6 inches
Division works just as well as multiplication when you flip the problem around.
Why This Matters
Rectangle area calculations show up constantly in real life:
- Calculating how much carpet you need
- Determining paint coverage for walls
- Figuring out tile quantities
- Measuring land parcels
- Sizing up furniture for a room
You don't need to be a math genius. You need to know how to multiply two numbers and keep track of your units.