Perimeter of compound shapes using Pythagoras' theory

Finding the perimeter of compound shapes using Pythagoras' theorem requires students to first identify the missing length (often a sloped edge or diagonal), then calculate it using a² + b² = c², and finally add all the sides to find the total perimeter.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • Pythagoras' theorem (a² + b² = c²)
  • hypotenuse
  • perimeter
  • compound shape
  • right angle
  • intermediate length
  • sloped edge

Task goals

  • Apply Pythagoras' theorem to find a missing edge in a compound shape
  • Calculate the perimeter by adding all sides together
  • Work with squares, rectangles, triangles, and parallelograms
  • Show working clearly in two steps (find the missing length, then the perimeter)
  • Use exact answers or round to 1 decimal place as required

Key skills

  • Pythagoras
  • Perimeter
  • Compound shapes
  • Find missing side

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included
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