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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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Not So Little X

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

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A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Square Areas

Age 11 to 14 Challenge Level:

The outer square has sides of length 1.

Can you work out the area of the inner square and give an explanation of how you did it?