Perimeter, area and volume
Rectangles, triangles, circles and cuboids
Perimeter is the distance around a shape. Area is the space inside it. Volume is the space inside a 3D shape.
Formulae to know
- Perimeter: add up all the sides.
- Rectangle area = length × width
- Triangle area = ½ × base × height
- Parallelogram area = base × height
- Circle: circumference = π × diameter; area = π × radius² (π ≈ 3.14)
- Cuboid volume = length × width × height
Units: perimeter in cm, area in cm², volume in cm³.
Worked examples
Example 1. A rectangle is 8 cm by 5 cm. Find its perimeter and area.
Example 2. A triangle has base 10 cm and height 6 cm. Find its area.
Example 3. A cuboid box is 6 cm by 4 cm by 3 cm. Find its volume.
Example 4. A circle has radius 5 cm. Find its area to 1 d.p.
Top tips and common mistakes
- Use the perpendicular height for triangles, not the sloping side.
- Diameter = 2 × radius. Read the question carefully to see which one you are given.
- For compound shapes, split them into rectangles and add the areas.
We worked out how much turf we needed for the garden using area. Dad was impressed!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Perimeter, area and volume worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.