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Thank-you to Clem, and to Marta & Brittany from MaST Community Charter School, and others who sent in solutions.
Seeing the image as a 'hole' surrounded by four rectangles, with each rectangle made from $2$ yellow (equilateral) and $2$ purple triangles.
The 'height' of the equilateral triangles is $\sqrt{3}$ divided by 2
So the dimensions of each rectangle are $1$ and $\sqrt{3}$
The side of the square hole is therefore $\sqrt{3} - 1$
The Square Hole
Age 14 to 16
Challenge Level 
Incidentally, did you notice that the yellow and purple triangles have the same area ? This doesn't require the particular case of one triangle being equilateral, any rectangle split into 4 areas by its diagonals will do.
More obvious now ?
Anyway back to the area of the Square Hole :
Thank-you to Clem, and to Marta & Brittany from MaST Community Charter School, and others who sent in solutions.
Seeing the image as a 'hole' surrounded by four rectangles, with each rectangle made from $2$ yellow (equilateral) and $2$ purple triangles.
The 'height' of the equilateral triangles is $\sqrt{3}$ divided by 2
So the dimensions of each rectangle are $1$ and $\sqrt{3}$
The side of the square hole is therefore $\sqrt{3} - 1$
