Regular polygons and circles

problem
Shedding some light

Age

7 to 11

Challenge level

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?
problem
Salinon

Age

14 to 16

Challenge level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
problem
What shape and colour?

Age

5 to 7

Challenge level

Can you fill in the empty boxes in the grid with the right shape and colour?
problem
Rolling around

Age

11 to 14

Challenge level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
problem
Overlapping circles

Age

7 to 11

Challenge level

What shaped overlaps can you make with two circles which are the same size?
problem
Lunar angles

Age

16 to 18

Challenge level

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?
problem
Circles in circles

Age

16 to 18

Challenge level

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
problem
The dodecahedron

Age

16 to 18

Challenge level

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?
problem
Shapely tiling

Age

7 to 11

Challenge level

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
problem
Semi-detached

Age

14 to 16

Challenge level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.