Using Pythagoras' Theorem on 3D Shapes

Pythagoras (top bloke), due to his love of mathematics and science was treated as a god in his time, a bit like Ed Sheeran is today.

Did you know that Pythagoras was in fact responsible for the musical scales we have today.

Imagine if Pythagoras' was headlining Glastonbury,  thousands of people hear him introduce his set as...

 'And my next number is ..........'

He had many followers (like Ed) who hung on to his every word, they thought his theories were magical.

Lets remind our self of his theory.

To find the Hypotenuse of a triangle

1. Square one side 2² = 4²

2. Square the other side 6² = 36²

3.  Add your answers together 36 + 4 = 40² 

4. √40 = 6.32 to 2 decimal places

To find a shorter side

1. Square the number on the hypotenuse 16 x 16 = 256 cm²

2. Square the number of the shorter side given 11 x 11 = 121 cm²

3. Subtract your answers 256 - 121= 135 cm²

4. Square root your answer √135 = 11.62 to 2 decimal places

Now Pythagoras (who ate, slept and drank mathematics) didn't want to end it there, oh no.  

He showed everyone how to apply this to 3D shapes. There is no end to his talent....

Calculating is just the same as normal, when working with a 2 dimensional triangle.

The trick here is being able to spot the triangle as shown in the example below.

To start

1. Draw the line BE onto the shape

2. Then draw in the BC and EC to form a right angled triangle.

To find the length of BE

• you need the length of BC which is given as 5 cm
• you need the length CE which is not given

Don't look so glum.  Pythagoras has given us some information to help us.

You can see that there is another right angled triangle given between C, E and F. We can use this to find the length CE

1. Square one side 5² = 25

2. Square the other side 5² = 25

3.  Add your answers together 25 + 25 = 50² 

4. √50 = 7.07 to 2 decimal places

Now we are ready to rock and roll

1. Square BC 5² = 25

2. Square EC 7.07² = 49.98

3.  Add your answers together 25 + 49.98 = 74.98² 

4. √74.98 = 8.66 to 2 decimal places

Did you know Pythagoras was one of the earliest people known to have given up eating meat for moral reasons?

Me neither.

Now you have an appetite for Pythagoras... lets go