### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

# Wood Pile Perimeter

##### Stage: 3 and 4 Short Challenge Level:

The centres of the three circles form an equilateral triangle, so each of the sectors marked is $\frac{1}{6}$ of a circle. The shape below is a rectangle, so the sectors are $\frac 14$ of a circle. The curved portion of the perimeters is therefore the same as each of the circles: $2\pi \times 5 = 10\pi \text{cm}$.

The straight part is the same length as two radii, so is $10\text{cm}$ long.

The perimeter of the shaded shapes is therefore $10+10\pi\text{cm}$.

This problem is taken from the UKMT Mathematical Challenges.
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