Area of a Rectangle

GCSE Geometry area rectangle
Practice this formula All formulas
\( A=\ell\,w \)

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.