Perimeter and Area of Plane Figures
77. Perimeter of a Square · Four equal sides, one simple rule
The perimeter is always 4 times the side length.
Perimeter of a square = 4 × side. All four sides equal, so just multiply the side length by 4: P = 4a.
What this lesson covers
Try to break it
A square's perimeter is always 4 times its side, no matter how you drag. Grab vertex A and try to break it — you'll see the numbers always match the formula. It never breaks!
How you build it
Construct a square with equal sides.
- Place point A, the first corner of the square.
- Place point B. The segment AB will be the first side of the square.
- Draw the segment from A to B.
- Construct a line through A, perpendicular to AB — this carries the next side.
- Set the compass opening to AB — click A, then B. The arc from A crosses the perpendicular.
- Mark point D where the arc crosses the perpendicular, above AB. Now AD = AB.
- With the compass still set to AB, draw an arc centred at B — click B.
- With the same opening, draw an arc centred at D — it crosses the arc from B.
- Mark point C where the arcs from B and D cross — the fourth corner.
- Draw the segment from B to C.
- Draw the segment from D to C. All four sides are equal and meet at right angles — ABCD is a square.
The proof, step by step
Prove that the perimeter of a square is 4 × side.
- A square has four equal sides.
- Perimeter is the sum of all sides.
- l + l + l + l = 4l.
Worked example
The side of a square is 12 cm. Find its perimeter.
Perimeter = 4 × side = 4 × 12 = 48 cm.
- 24 cm
- 36 cm
- 48 cm — correct
- 144 cm