Learn: Perimeter & Area

A quick, calm intro — then you choose when to climb.

The idea

Perimeter is the fence around the outside; area is the floor inside. Same rectangle, two different jobs.

The rules:

1
Perimeter — the fence around the outside — add all the sides (metres)
2
Area — the floor inside — for a rectangle, length × width (square metres)
3
Units differ — metres vs square metres — they measure different things

Quick memory tips

Go all the way around: 2 lengths + 2 widths
Fences are m, floors are m² — the unit tells you which one you found
Same rectangle, two answers — one around, one inside

Perimeterunit: m

The fence walking around the shape.

P = 2(l + w)

Areaunit: m²

The floor covering the inside of the shape.

A = l \times w

Other common shapes (Area)

Square

A = s^{2}

Triangle

A = \tfrac{1}{2}bh

Parallelogram

A = b \times h

Circle

A = \pi r^{2}

Trapezoid

A = \tfrac{1}{2}(a+b)h

Right Triangle

A = \tfrac{1}{2}bh

Green fill = area (inside). Blue dashed line = height helper. Main lesson: perimeter is around, area is inside.

Blue = the fence walking around the outside (perimeter, metres). Green = the floor filled inside (area, square metres). Two views of the same rectangle — and the same ideas extend to every shape below.

Worked example

Every step explained — why we do it, and what happens.

1
$\text{length } 4 \text{ m, width } 6 \text{ m}$
Why: Name the shape and its sides: opposite sides of a rectangle are equal — two 4s and two 6s.
What happens: A 4-by-6 rectangle.
2
$P = 2(4 + 6) = 20 \text{ m}$
Why: Perimeter is the fence: go all the way around — 4 + 6 + 4 + 6, or 2 × (4 + 6).
What happens: 20 m of fence.
3
$A = 4 \times 6 = 24 \text{ m}^2$
Why: Area is the floor: length × width. Square metres, because metres × metres.
What happens: 24 m² of floor.
4
$P = 20 \text{ m}, \quad A = 24 \text{ m}^2$
Check the units: the fence is metres, the floor is square metres. They measure different things — that is the whole trick.

Real-world example

The school garden has a rectangular bed 5 m long and 3 m wide. How much fencing goes all the way around it, and how much soil area is inside?

1
$5 \text{ m by } 3 \text{ m}$
Why: A rectangle: two pairs of equal sides — two 5s and two 3s.
What happens: The garden bed.
2
$P = 2(5 + 3) = 16 \text{ m}$
Why: The fence goes all the way around: 2 lengths + 2 widths.
What happens: 16 m of fencing.
3
$A = 5 \times 3 = 15 \text{ m}^2$
Why: The soil covers the inside: length × width.
What happens: 15 m² of soil.
4
$\text{Trap: } 5 + 3 = 8 \text{ m}$
Why: The glitch: 5 + 3 adds only two sides — that would fence just half the bed. All the way around: 2(5 + 3) = 16 m.
What happens: Right: 2(5 + 3) = 16 m — all the way around.
5
$2(5 + 3) = 16, \qquad 5 \times 3 = 15$
Why: The check: fence = around = 16 m; soil = inside = 15 m². Different jobs, different units.
What happens: 16 m of fence, 15 m² of soil ✓

Common glitch

Two classic glitches:

1.Perimeter vs area mix-up

Wrong:Fence = 15 m² — using area for the fence

Right:Fence = perimeter (m): 16. Soil = area (m²): 15.

2.Forgetting to go all the way around

Wrong:5 + 3 = 8 m of fence

Right:Two lengths + two widths: $2(5 + 3) = 16$ m.

Area and Perimeter Calculator — Calculate area and perimeter for common shapes.
Unit Converter — Convert measurements before using a shape formula.

Next up: Circles →

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Learn: Perimeter & Area

The idea

The rules:

Quick memory tips

Other common shapes (Area)

Worked example

Real-world example

Common glitch

Try a related calculator

Learn: Perimeter & Area

The idea

The rules:

Quick memory tips

Other common shapes (Area)

Worked example

Real-world example

Common glitch

Try a related calculator