Find the Area of a Rectangle
Complete Guide with Formula, Calculator & Real-World Examples
What is the Area of a Rectangle?
The area of a rectangle is the amount of space occupied by the rectangle within its boundary[web:81][web:82]. It represents the two-dimensional region enclosed by the four sides of the rectangle and is measured in square units such as square meters (\( m^2 \)), square centimeters (\( cm^2 \)), square feet (\( ft^2 \)), or square inches (\( in^2 \))[web:84].
A rectangle is a four-sided polygon (quadrilateral) with the following properties[web:89]:
- Opposite sides are equal in length
- All four interior angles are right angles (90°)
- Has two dimensions: length and width (or breadth)
- Diagonals are equal in length and bisect each other
Understanding how to calculate the area of a rectangle is fundamental in mathematics and essential for numerous real-world applications including construction, interior design, agriculture, and engineering[web:86][web:89].
Area of Rectangle Formula
The formula to calculate the area of a rectangle is simple and elegant[web:81][web:82][web:84]:
where \( l \) is the length and \( w \) is the width (or breadth \( b \))
Understanding the Components:
• Length (l)
The longer side of the rectangle, measured in units such as meters, centimeters, feet, or inches[web:82].
• Width or Breadth (w or b)
The shorter side of the rectangle, measured in the same units as length[web:82][web:84].
• Area (A)
The result of multiplying length by width, expressed in square units[web:81][web:82].
🧮 Rectangle Area Calculator
Calculate Area = Length × Width
Enter the length value
Enter the width value
Quick Examples to Try:
Formula Derivation
The area formula can be derived by dividing the rectangle into two equal right-angled triangles using a diagonal[web:84][web:91]:
Step 1: Divide the rectangle
When you draw a diagonal in a rectangle, it divides the rectangle into two congruent right-angled triangles[web:84].
Step 2: Calculate triangle areas
Area of each triangle = \( \frac{1}{2} \times \text{base} \times \text{height} \)
Area of each triangle = \( \frac{1}{2} \times l \times w \)
Step 3: Combine both triangles
Area of rectangle = 2 × (Area of one triangle)
Area of rectangle = \( 2 \times \left(\frac{1}{2} \times l \times w\right) \)
Area of rectangle = \( l \times w \)
Therefore: \( A = l \times w \) ✓
How to Calculate the Area of a Rectangle
Follow these simple steps to find the area of any rectangle[web:82][web:84]:
Step 1: Identify the Dimensions
Note the length and width of the rectangle from the given information. Make sure both measurements are in the same units[web:82][web:84].
Step 2: Multiply Length by Width
Calculate the product of the length and width values[web:81][web:82].
Step 3: Express in Square Units
Write your answer with the appropriate square units (e.g., \( m^2 \), \( cm^2 \), \( ft^2 \))[web:82][web:84].
Worked Examples
Example 1: Basic Calculation
Problem: Find the area of a rectangle with length 15 cm and width 4 cm[web:82][web:89].
Solution:
Given: Length = 15 cm, Width = 4 cm
Formula: Area = Length × Width
Area = 15 cm × 4 cm
Area = 60 cm²
Answer: The area is 60 square centimeters
Example 2: Real-World Application
Problem: A rectangular carpet is 2.5 meters long and 1.2 meters wide. What is its area?[web:89]
Solution:
Given: Length = 2.5 m, Width = 1.2 m
Area = 2.5 m × 1.2 m
Area = 3.0 m²
Answer: The carpet covers 3.0 square meters
Example 3: Finding Missing Dimension
Problem: A rectangle has an area of 180 cm² and length 15 cm. What is the width?[web:81][web:89]
Solution:
Given: Area = 180 cm², Length = 15 cm
Formula: Width = Area ÷ Length
Width = 180 cm² ÷ 15 cm
Width = 12 cm
Answer: The width is 12 centimeters
Example 4: Using Diagonal
Problem: A rectangle has a diagonal of 13 cm and length of 5 cm. Find its area[web:81][web:89].
Solution:
Given: Diagonal = 13 cm, Length = 5 cm
Using Pythagorean theorem: Width = \( \sqrt{\text{diagonal}^2 - \text{length}^2} \)
Width = \( \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \) cm
Area = Length × Width = 5 cm × 12 cm = 60 cm²
Answer: The area is 60 square centimeters
Related Formulas for Rectangles
Perimeter of Rectangle
The perimeter is the total distance around the rectangle[web:87][web:90]:
Where P is perimeter, l is length, and w is width[web:90][web:93].
Diagonal of Rectangle
Using the Pythagorean theorem[web:81]:
Where d is the diagonal length.
Finding Missing Side
When area is known[web:81]:
Real-World Applications
Calculating the area of rectangles is essential in numerous everyday situations and professional fields[web:86][web:89][web:95]:
🏗️ Construction & Architecture
Calculating floor space, wall areas for painting, roofing materials, and determining room dimensions[web:86][web:97].
🎨 Interior Design
Measuring spaces for carpet, tile, wallpaper, and furniture placement planning[web:89][web:99].
🌾 Agriculture & Farming
Calculating field areas for crop planning, irrigation coverage, and land management.
🌳 Gardening & Landscaping
Determining garden bed sizes, lawn areas, and material needs for landscaping projects[web:97].
⚽ Sports Fields
Designing and measuring playing fields for football, basketball, tennis courts, and other rectangular sports areas[web:86].
📦 Packaging & Shipping
Calculating box sizes, label dimensions, and optimizing packaging materials[web:86].
🪵 Carpentry & Woodwork
Measuring wood panels, tabletops, door sizes, and cutting materials accurately[web:86].
🏫 Education
Teaching geometry, spatial reasoning, and practical mathematics applications[web:95].
🖼️ Art & Design
Canvas sizes, picture frames, poster dimensions, and graphic design layouts[web:86].
🏠 Real Estate
Measuring property sizes, room areas for listings, and land valuation.
Important Facts & Tips
💡 Unit Consistency
Always ensure length and width are in the same units before multiplying. Convert if necessary (e.g., 1 meter = 100 centimeters)[web:82][web:89].
💡 Square Units
Area is always expressed in square units. If dimensions are in meters, area is in square meters (\( m^2 \))[web:81][web:84].
💡 Square Special Case
A square is a special rectangle where all sides are equal. Its area is \( \text{side}^2 \)[web:81][web:90].
💡 Commutative Property
Length × Width = Width × Length. The order doesn't matter when multiplying[web:82].
💡 Area vs Perimeter
Area measures the space inside, perimeter measures the distance around. Two rectangles can have the same area but different perimeters[web:87][web:98].
💡 Maximum Area
For a given perimeter, a square has the maximum area among all rectangles[web:87].
💡 Historical Note
Ancient Egyptians and Babylonians used rectangle area calculations for land measurement and architecture over 4000 years ago.
💡 Curriculum Coverage
Rectangle area appears in primary mathematics, IB Math, AP Geometry, GCSE/IGCSE Mathematics, SAT Math, and all international curricula.
Practice Problems
Problem 1
A rectangular garden measures 25 meters in length and 12 meters in width. Calculate its area.
Problem 2
A classroom floor has an area of 72 square meters. If the length is 9 meters, what is the width?
Problem 3
A rectangular picture frame is 30 cm long and 20 cm wide. How much glass is needed to cover the picture?
👨🏫 About the Author
Adam
Co-Founder @RevisionTown
Math Expert in various curricula including IB, AP, GCSE, IGCSE, and more.