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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Equilateral Areas

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

Square Pizza

Age 14 to 16
Challenge Level

You probably need to consider the two people having alternate segments of the pizza.

You could consider the areas of all the right angled isosceles triangles.

Alternatively, you could reduce the problem considerably by removing a symmetrial portion of the pizza.