Perimeter of a Square

GCSE Geometry perimeter square
Practice this formula All formulas
\( P=4s \)

Statement

The perimeter of a square is the total distance around it. Since a square has four equal sides of length \(s\), the perimeter is:

\[ P = 4s \]

Why it’s true

  • A square has 4 equal sides.
  • Adding all sides together gives \(P = s + s + s + s = 4s\).

Recipe (how to use it)

  1. Identify the side length \(s\).
  2. Multiply the side length by 4.
  3. The result is the perimeter.

Spotting it

This formula is used whenever the shape is a square, and the question asks for the distance around it (perimeter).

Common pairings

  • Square fencing or boundary problems.
  • Comparisons between square perimeters and areas.
  • Scaling and enlargement problems.

Mini examples

  1. Given: Side = 6. Find: Perimeter. Answer: \(P=4(6)=24\).
  2. Given: Side = 12. Find: Perimeter. Answer: \(P=4(12)=48\).

Pitfalls

  • Forgetting that all sides are equal.
  • Mixing perimeter with area (\(A=s^2\)).

Exam strategy

  • Write formula \(P=4s\) before substituting values.
  • If perimeter is given and side length is needed, rearrange: \(s=P/4\).
  • Always check units (cm, m, km).

Summary

The perimeter of a square is four times the side length: \(P=4s\). Simple, but commonly tested in foundation problems and as part of multi-step geometry questions.