Length and area

Length tells you how far it is from one point to another, and area tells you how much flat space a shape covers. In this topic you'll convert between metric units, find the perimeter of simple and composite shapes, and learn the rules for the area of rectangles, triangles and parallelograms. You'll finish by discovering the number π and using it to find the distance around a circle. Builders, farmers, painters and designers use these skills every day.

What you'll learn

• 12.01 Units of length: millimetres, centimetres, metres and kilometres, reading a ruler, and converting from one unit to another.
• 12.02 Perimeter: the distance around a shape, a rule for the perimeter of a rectangle, and finding a missing side.
• 12.03 Perimeter of composite shapes: finding missing sides and the perimeter of shapes made by joining simpler shapes.
• 12.04 Area of rectangles and squares: square units such as cm² and m², and the rule A = l × w.
• 12.05 Area of triangles: base and perpendicular height, and the rule A = ½ × b × h.
• 12.06 Area of parallelograms: turning a parallelogram into a rectangle, and the rule A = b × h.
• 12.07 Area of composite shapes: splitting shapes into parts, adding areas, and subtracting pieces that have been cut out.
• Investigation: explore circles. Measure round objects and discover the special number π that links the distance around a circle to the distance across it.
• 12.08 Circumference of a circle: radius, diameter and the rule C = π × d, with the π key on your calculator.

Which level should I pick?

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

• Level 1 · Warm-up: whole numbers, labelled diagrams and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: decimals, mixed units, exact answers and problems with more steps, 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.