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Learn · Numeracy · 5 min

Area, perimeter & volume, from scratch

Three measures people mix up — really it’s one idea in 1D, 2D and 3D:

See it: area fills, perimeter surrounds

■ Area = 6 × 4 = 24 cm²
▢ Perimeter = 2 × (6 + 4) = 20 cm

Flat shapes: multiply for area, add for perimeter

  • Area = length × width → square units (cm²).
  • Perimeter = 2 × (length + width) → a plain length (cm).
  • A 6 × 4 rectangle: area = 24 cm², perimeter = 20 cm.

Now go 3D — volume

Stack that flat shape up into a solid. Volume counts the little cubes that fill it.

See it: volume is the space a solid fills

543

Volume = 3 × 5 × 4 = 60 cubes (cm³)
= area of the base (5 × 3 = 15) × height (4)

The one move: length × width × height

  • Work out the base first (length × width), then stack it up by the height.
  • A 2 × 3 × 4 box → 2 × 3 × 4 = 24 cm³.
  • Volume is always in cubic units (cm³).

Tips & tricks

Rectangle
Area = length × width  ·  Perimeter = 2 × (length + width)
Square
Area = side × side  ·  Perimeter = 4 × side
Box (cuboid)
Volume = length × width × height  ·  Cube = side × side × side
Odd shapes → split into rectangles
Break an L-shape into two rectangles, find each area, then add them together.
Units tell you which is which
Perimeter → cm  ·  Area → cm²  ·  Volume → cm³

Now you try — 0/3

1. A rectangle is 6 cm long and 4 cm wide. What is its AREA (in cm²)?

2. The same 6 cm × 4 cm rectangle — what is its PERIMETER (in cm)?

3. A box is 2 cm × 3 cm × 4 cm. What is its VOLUME (in cm³)?

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