### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

# Weekly Problem 43 - 2009

##### Stage: 2 and 3 Short Challenge Level:

The diagram has rotational symmetry of order four about $D$.

If angle $ABC$ is $15^{\circ}$ and the area of $ABEF$ is $24$cm$^2$, what, in cm, is the length of $CD$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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