Measurement

Measurement is maths you can hold in your hands: the fence around a paddock, the paint for a wall, the water in a tank. In this topic you'll find the perimeter and area of all sorts of shapes, including circles and shapes built from several pieces, learn why $\pi$ turns up in every circle, and work out how much space a prism takes up and how much it can hold.

What you'll learn

• 9.01 Perimeter: a refresher on the distance around a shape, regular polygons and converting units of length.
• 9.02 Circumference of a circle: C = $\pi$ × d and C = 2 × $\pi$ × r, answers in terms of $\pi$, and why $\pi$ is irrational.
• 9.03 Perimeter of composite shapes: missing sides, and shapes with semicircles, quadrants and other arcs.
• 9.04 Estimation and units of area: choosing and converting mm², cm², m², hectares and km², and estimating the area of irregular shapes.
• 9.05 Area of rectangles, triangles and parallelograms: a refresher on the formulas and the perpendicular height.
• 9.06 Area of composite shapes: adding and subtracting areas to find the area of shapes made of several parts.
• 9.07 Area of trapeziums, kites and rhombuses: the trapezium formula, and finding area from the diagonals.
• Investigation: the area of circles. Count squares, then cut a circle into slices and rearrange them to discover A = $\pi$ × r².
• 9.08 Area of a circle: using A = $\pi$r² for circles, semicircles and quadrants, and working backwards to the radius.
• 9.09 More composite areas: shapes with circles, sectors and rings, and shaded regions.
• 9.10 Units of volume and capacity: mm³, cm³ and m³, millilitres, litres and kilolitres, and how they connect.
• 9.11 Volume of right prisms: volume = area of the cross-section × height, for rectangular, triangular and other prisms.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: harder numbers and multi-step problems, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.