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Square Areas

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

Square Pegs

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

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?

Bow Tie

Age 11 to 14 Challenge Level:
Thanks to Hannah, Sophie Rebecca of the Roos C.E Primary School, who sent in the beginnings of a solution but there is still much to do. I have added some comments below.


Firstly, we decided that we should use the rightangles on the shape to create a 360 degree pattern. We found that the pattern made a shape of a butterfly. We also found out that the butterfly pattern could be joined together.

 

Basic unit

What transformations of the original tile were needed to create this unit?
How do these basic units fit together to tessellate the plane?
What other transformations of the original tile are needed to cover the plane?