# Diagonal Side

Can you work out the area of a square drawn on a diagonal?

The diagonal of a unit square is used as one of the sides of a new square.

What is the area of this new square?

(A unit square is a square whose sides all have length 1 unit, and so its area is 1 square unit)

What is the area of this new square?

(A unit square is a square whose sides all have length 1 unit, and so its area is 1 square unit)

*This problem is taken from the World Mathematics Championships***Measuring using unit squares**

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The area of the square is shaded in the diagram on the right. It contains four half-unit-squares - so its area is four half-units, or two whole units.

**Using Pythagoras' Theorem to find the side length**

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Applying Pythagoras' Theorem to the triangle will give us information about this length, here called $c$: $1^2+1^2=c^2\Rightarrow2=c^2$

But $c^2$ is the area of the square with side length $c$. So if $c^2=2$, then the area is $2$.