### 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?

### Towers

A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

### Framed

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

# Fence It

##### Age 11 to 14 Challenge Level:

Imagine you had $40$ one-metre sections of fencing.

What is the largest rectangular area of land you could fence off?

Now imagine you could build your fence up against a wall, so you only need to use the fence for three sides of the enclosure:

What is the largest area you can fence off now?

Now imagine you can attach the fence to the wall shown below, at the point marked X.

What is the largest area you can fence off now?

Extension
Could you enclose even greater areas if you had $40$m of flexible wire fencing that could fence off curves as well as straight lines?