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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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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?

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Bull's Eye

What fractions of the largest circle are the two shaded regions?

Squaring the Circle

Age 11 to 14 Challenge Level:

Bluey - green squares, white squares, transparent squares with a few odd bits of shapes around the perimeter.

Picture of a circular area tiled with squares

But, how many squares are there of each type in the complete circle?

Study the picture and make an estimate. Note the totals before embarking on a more rigorous audit of what is there.

How accurate was your estimate?

Can you give an upper and a lower bound to your estimate?

If the blue-green squares are of 1 and 1.5 units of length, the white squares of 1.5 units and the transparent squares 1.75 units of length - how "big" is the circular part of the pavement?