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This is what Fiona says:
The first thing I did was to get some squared paper to draw the figure on. I found out I couldn't start the middle square as one square because I couldn't draw the other squares accurately so I did the middle square as a four and that gave me points for the rest of the figure.
To find the total area of the numbered triangles:
I noticed that $1$ and $4$ were two halves of a square and
also $2$ and $3$ are two halves of a square.


Now I just have to count every square in this top rectangle as one unit: My answer is $32$ square units. 
Courtney, Charlotte and Tyler from Gateway Primary also used this approach.
Here is what Douglas did:
Gemma and Nathalie from City of London Freemen's School, Roger, Mark and Sam from Spalding Grammar School and George from Strand on the Green Juniors also noticed this pattern and so they didn't need to do any drawing to find the solution. Nathalie wrote:
Well done too to Callum from Arthur Mellows Village College and children from Truscott Street Public School.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?