In this activity, we are going to use what we know about Pythagoras' Theorem to find the length of the **hypotenuse** in a right-angled triangle.

*You will need a calculator for this activity!*

__Recap__

If we add the areas of the two shorter sides together, they fit exactly into the square of the diagonal side.

The area of that square is **5 x 5 = 25 cm ^{2}**

**16 cm ^{2} + 9 cm^{2} = 25 cm^{2}**

We call the diagonal side, opposite the right angle the **hypotenuse**.** **

If we know the two shorter sides we can work out the area on the **hypotenuse!**

If we square root this, we get the **length of the hypotenuse!**

Let's try a question without drawing the squares!

__Example__

Calculate the **length** of the missing side (hypotenuse, H) below.

**Answer**

Remember the missing hypotenuse can be found because:

## The shorter sides squared and added together = hypotenuse squared

In short:

**6 ^{2 }+ 8^{2 }= H^{2}**

**36 + 64 = H ^{2}**

**100 = H ^{2}**

**H = the square root of 100**

**H = 10**

*This is the button on the calculator which works out the square root for you.*

Let's try some more like this!