Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
A man paved a square courtyard and then decided that it was too
small. He took up the tiles, bought 100 more and used them to pave
another square courtyard. How many tiles did he use altogether?
Can you work out the area of the inner square and give an
explanation of how you did it?
Laura Turner and Laura Malarkey from the Mount
School have explained how they worked out the answer to this
n is equal to the number of tiles along one side.
We can calculate the number of edges in two different ways:
Method 1 - In total there are $n²$ tiles on
Method 2 - There are a total of $2n$ green edges which implies
there are a total of $20n$ edges of all colours.
$20n = 4n²$
$5n = n²$ (divide by $4$)
$5 = n$ (divide by $n$)
So there are $25$ tiles in the set.