About this worksheet

This free Year 8 Pythagoras’ theorem worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MMGTW3. It targets one skill so students can practise until it sticks: by the end, students can say “I can identify the hypotenuse and use Pythagoras’ theorem to find its length, exactly or rounded.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Identifying the hypotenuse
• Using c² = a² + b² to find the hypotenuse
• Recognising Pythagorean triples

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 58, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Forgetting to square root at the end
• Adding the sides before squaring
• Squaring decimals incorrectly, e.g. 0.9² = 8.1
• Choosing a side that isn't opposite the right angle

Where this fits in the WA Year 8 sequence

Pythagoras’ Theorem: Finding the Hypotenuse sits in the Two-dimensional space and structures sub-strand of Measurement and geometry. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Forgetting to square root at the end
• Adding the sides before squaring
• Squaring decimals incorrectly, e.g. 0.9² = 8.1
• Choosing a side that isn't opposite the right angle