Numerical aptitude · Shapes and data
Area and volume, made easy
💡 The idea
Perimeter is the edge (a length, in m). Area is the inside, counted in squares (m²). Volume is the space, counted in cubes (m³).
📏 perimeter
round the edge→⬛ area
squares inside→🧊 volume
cubes inside
round the edge→⬛ area
squares inside→🧊 volume
cubes inside
🧭 The method: 3 steps
- Draw the shape and write the measurements on it.
- Pick the right formula (below), keeping all units the same.
- Check the units: m for edges, m² for area, m³ for volume.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
Loading the pictures…
✏️ Worked examples
Example 1. Rectangle 8 m × 5 m: area and perimeter?
- Area = 8 × 5 = 40 m²
- Perimeter = 2 × (8 + 5) = 26 m
Example 2. Circle of radius 7 cm: area?
- π r² = 22/7 × 7 × 7
- = 154 cm²
Example 3. Garden 10 × 6 with a 1 m path round it: path area?
- With path: 12 × 8 = 96
- Garden: 60
- Path = 36 m²
⚠️ Where people go wrong
- Mixing up area (inside) and perimeter (edge).
- Using the diameter where the radius is needed.
- A path all round adds to BOTH sides: + 2 × width.
📌 Remember
- Rectangle: l × w, 2(l + w)
- Triangle: ½ b h
- Circle: π r², 2 π r
- Box: l w h
- Cylinder: π r² h