Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Solve Complex problems Using Pythagoras' Theorem

In this worksheet, students will apply Pythagoras' theorem to solve more problems.

'Solve Complex problems Using Pythagoras' Theorem' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Eduqas, AQA, OCR, Pearson Edexcel,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview


We already know that our friend Pythagoras here, had the brain the size of a planet.

He must have as it is said that he never wrote any of his theories down.

wooly hat

Let us put our thinking cap on the revise the theorem

Remember this theorem only works for right-angled triangles.

To find the hypotenuse (longer side) of a triangle


right angles triangle without hypotenuse length


10² + 3² =  √109 = 10.44 cm to 2 decimal places



To find the shorter side length

right angled triangle with shorter side length missing

9² - 7² =√32 = 5.66 to 2 decimal places


The key point here is to remember when to add and when to subtract.

We can apply this to solve all sorts of problems. However they may be presented.


Question 1

The diagonal of a square is 10 cm long.  What is the length of one side of the square?

sketch book


Pythagoras problem

Now don't be tempted to think because this is a square it will be 10 cm.

Pythagoras gave us his theorem for a reason.        

Here you can see a right angled triangle has been formed.

We know that ?² + ?² = 10² (100 cm)

The sides will both be the same length as we are looking at a square.

100 ÷ 2 = 50 cm² √ 50 cm² = 7.07 cm rounded to 2 decimal places


Question 2


Pythagoras algebrapythagoras complex solution





You are always looking to sketch the situation out to turn a diagram into a right angles triangle.

In more complex problems you will need to draw on other knowledge too.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Try an activity or get started for free

  • educational
  • bettfutures
  • cxa
  • pta
  • era2016
  • BDA award
  • Explore LearningTuition Partner
  • tacm