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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.

Rhombus in Rectangle

Age 14 to 16 Challenge Level:

Call the base of the rectangle $b$ and the height $h$. If the distance from A to P is $x$, can you write an equation linking $b$, $h$ and $x$ in order to make $AP=PQ$? How many possible values can x take in your equation?