You may also like

problem icon

At a Glance

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

problem icon

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?

problem icon


Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

From All Corners

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Straight lines are drawn from each corner of a square to the mid points of the sides which are opposite, as shown.

Express the area of the octagon as a fraction of the area of the square.