Hay folk! My name is Pythagoras. Today I’m going to teach you how to solve my life’s work.

You can take any right angle triangle and use Pythagoras theorem on it.

Now, in Pythagoras there is one formula you have to learn and remember or you wont ever know how to work out my theorem. It is a²+b²=c². A and B are always the smaller of the three. And C is always bigger.

AC

B

Remember you have to square them!!!

A²C²

B²

Now let’s make a massive jump and make a 3D cuboid!In a cuboid there are loads of right angle triangles, see.

Let use the bottom one. If we know the width (3) and the depth (5) of the cuboid we can put the formula into practice and work out the longest line of the triangle.

3

5

Get a scientific calculator and try to work it out.Don’t forget to square them!

3

5

That’s right it’s 34!Now we square root them to get a smaller answer.

3

5

You got it. It’s 5.83. you always round to two decimal places unless the questions asks you other wise.

6

5

3

Look there’s another right angle triangle!Now if we know that the height is 6 and we have worked out the diagonal at the bottom, we can work out the diagonal across the cuboid!

Have a go! Work out the length of the diagonal across the middle of the cuboid.Remember: a²+b²=c²And square root it!

6

5.83

Yip! You got it! It’s 1192Now remember you have to square root it!

Yip! Yip! Yip! 34.53.

Wow! You’re smart! Smarter that Lord Smarticus himself!

Work out this diagonal!Work out the fractions, round them up to three decimal place and don’t forget to square the sides! And to square root the finished product!

8

2

3

That’s right.!

Wow, that was difficult but you did it. You have become a junior mathematician! Carry on and you will be a pro!!!Thanks and Good bye!