How to Find the Area of a Rectangle: Step-by-Step Guide
The Area of Rectangles Formulas is a key concept in geometry and measurement, helping students calculate how much surface a rectangle covers. Knowing this formula is crucial for tackling questions in school exams, competitive tests, and everyday tasks like finding the size needed for paint, tiles, or paper. Let's explore how to use and apply the area of rectangles formula in various mathematical situations.
Understanding the Area of a Rectangle
A rectangle is a four-sided shape (quadrilateral) with opposite sides equal and all four corners as right angles (90°). The area of a rectangle refers to the "total space inside" its boundaries, measured in square units such as cm² or m². Calculating rectangular area is important for tasks in construction, design, land management, and exams.
- Opposite sides are equal length
- All angles are 90°
- Has two dimensions – length (l) and width/breadth (w or b)
Area of Rectangle Formula
The main formula to calculate the area of a rectangle is:
or, A = l × w
Where:
- A = Area of rectangle (in square units)
- l = Length of rectangle
- w = Width (or Breadth) of rectangle
If the diagonal (d) and one side (length or width) are given, use Pythagoras’ theorem to find the missing side:
Length = √(diagonal² – width²)
If diagonal and length are known:
Width = √(diagonal² – length²)
Step-by-Step Examples
Let’s see the rectangle area formula in action with a few worked examples:
-
Find the area of a rectangle with length 15 cm and width 4 cm:
Area = 15 cm × 4 cm = 60 cm² -
A rectangular carpet is 2.5 m long and 1.2 m wide. What is its area?
Area = 2.5 m × 1.2 m = 3.0 m² -
A rectangle's area is 180 cm². Its length is 15 cm. What is the width?
Width = Area ÷ Length = 180 cm² ÷ 15 cm = 12 cm -
The diagonal of a rectangle is 13 cm, and the length is 5 cm. Find the width.
Using: Width = √(diagonal² – length²)
Width = √(13² – 5²) = √(169 – 25) = √144 = 12 cm
Practice Problems
- Calculate the area of a rectangle with length 9 cm and width 7 cm.
- If the area of a playground is 450 m² and the width is 15 m, find its length.
- The diagonal of a rectangle is 10 cm and the width is 6 cm. What’s the length?
- A piece of paper is 21 cm long and 14 cm wide. Find its area.
- A garden is 25 m by 12 m. How much area does the garden cover?
Common Mistakes to Avoid
- Mixing up perimeter and area (perimeter adds up the sides; area multiplies length by width).
- Forgetting to write square units (e.g., 30 instead of 30 cm²).
- Not converting measurements to the same unit before multiplying (always use either all cm, all m, etc.).
- Confusing length and width; order does not matter in multiplication, but both dimensions should be from the rectangle.
Real-World Applications
The area of rectangles formula is used in tasks like:
- Calculating how much paint is needed for a wall.
- Finding how many tiles to cover a floor.
- Estimating the area of land or garden beds.
- Determining paper or poster sizes in design and printing.
- Cutting fabric or cardboard into desired shapes for projects.
At Vedantu, we teach these applications with visuals and examples, making calculations easy for daily life and exams.
Connections to Other Shapes
It's helpful to compare rectangle area formulas with those of related shapes:
| Shape | Area Formula |
|---|---|
| Rectangle | Length × Width (l × w) |
| Square | Side × Side (s²) |
| Triangle | ½ × Base × Height |
| Parallelogram | Base × Height |
| Trapezium | ½ × (Sum of parallel sides) × Height |
Learn more about Area of Square, Perimeter of Rectangle, and other Geometry Formulas on Vedantu.
Summary: The area of rectangles formula (Area = Length × Width) helps you find the space inside any rectangle quickly and accurately. Always use the correct units, double-check for mix-ups with perimeter, and practice with problems on Vedantu for complete confidence in geometry!
FAQs on Rectangle Area Formula Made Simple
1. How to find the area of a rectangle?
The area of a rectangle is found by multiplying its length and width. This fundamental geometry concept is crucial for various applications.
2. What are the formulas for area?
The basic formula for the area of a rectangle is: Area = length × width. Other shapes have different formulas. For a square, it's side × side. For a triangle, it's ½ × base × height. Knowing these mensuration formulas is key to solving area problems.
3. How to calculate the area of land with 4 unequal sides?
Land with four unequal sides is not a rectangle; it's a quadrilateral. You'll need more information, like the diagonals or the ability to break it into smaller rectangles or triangles to calculate the area. You might use techniques from coordinate geometry.
4. How to find the area of two rectangles?
Calculate the area of each rectangle individually using the formula Area = length × width. Then, add the two areas together to find the total area.
5. What is the standard area formula for a rectangle?
The standard formula is Area = length × width. Remember to use consistent units (e.g., cm², m²) throughout your calculation.
6. Which units are used for rectangle area?
Area is always measured in square units. Common units include square centimeters (cm²), square meters (m²), square kilometers (km²), and square feet (ft²). The choice depends on the scale of the rectangle.
7. How do I find the area of a rectangle with a diagonal?
If you know the diagonal (d) and one side (l or w), you can use trigonometry or the Pythagorean theorem to find the other side, and then use the standard formula Area = length × width. Alternatively, some advanced formulas directly involve the diagonal but are less commonly used.
8. What is the difference between area and perimeter?
Area measures the space inside a shape, while perimeter measures the distance around the shape. For a rectangle, area is length × width, and perimeter is 2(length + width). They're both important geometric concepts but measure different properties.
9. Is there a shortcut to remember area formulas?
Visual aids and practice are best. Create flashcards or diagrams. Focus on understanding the underlying logic rather than rote memorization. Relating area formulas to real-world examples (like calculating floor space) can help too.
10. How is the rectangle area formula related to square area?
A square is a special type of rectangle where all sides are equal. Therefore, the area formula for a square (side × side) is a simplified version of the rectangle area formula (length × width). Understanding this relationship can help you solve problems for both shapes.
11. What is the area of rectangle formula class 7?
In class 7, the primary rectangle area formula taught is Area = length × width. This is a foundational concept in geometry and mensuration.
12. What is the area of rectangle formula class 5?
Class 5 typically introduces the basic area of a rectangle formula: Area = length × width. This is often presented using visual aids and practical examples.
13. Area of rectangle formula with diagonal?
While there isn't a direct formula using only the diagonal, you can find the area if you know the diagonal and one side. Use the Pythagorean theorem (a² + b² = c² where 'c' is the diagonal) to calculate the missing side and then apply the standard Area = length × width.
