Area of a Rectangle

Statement

The area of a rectangle is given by:

\[ A = l \times w \]

Here, \(A\) is the area, \(l\) is the length, and \(w\) is the width (sometimes called breadth).

Why it’s true (short reason)

• A rectangle is made up of rows of unit squares.
• If there are \(l\) units across and \(w\) units down, the total number of squares is \(l \times w\).
• This gives the formula for area: base × height (length × width).

Recipe (how to use it)

1. Identify the rectangle’s length and width (sides at right angles).
2. Multiply the two values.
3. Attach the correct units squared (e.g., cm², m²).

Spotting it

• Questions that use the word “rectangle” or “oblong”.
• Composite shapes where a rectangle is part of the figure.
• Tables, fields, or rooms often described in real-life contexts.

Common pairings

• Perimeter of rectangle: \(2l+2w\).
• Area of square: special case where \(l=w\).
• Volume of cuboid: area of rectangle × height.

Mini examples

1. Given: l=8 cm, w=5 cm. Find: area. Answer: 40 cm².
2. Given: l=12 m, w=4 m. Find: area. Answer: 48 m².

Pitfalls

• Mixing perimeter with area: perimeter adds sides, area multiplies them.
• Wrong units: always use squared units for area.
• Using diagonal instead of width: only length and width (at right angles) are valid.

Exam strategy

• Underline whether the question asks for area or perimeter.
• Write the formula before substitution.
• Check both sides are in the same units before multiplying.

Summary

The area of a rectangle is length × width. This is one of the simplest and most frequently used formulas in geometry, with countless applications in real life and mathematics.