### 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?

### Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

### Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

# Isometric Areas

##### Stage: 3 Challenge Level:

Here is an equilateral triangle with sides of length 1.

Let's define a unit of area, $T$, such that the triangle has area $1T$.

Here are some parallelograms whose side lengths are whole numbers.

Can you find the area, in terms of $T$, of each parallelogram?
Compare the results with the lengths of their edges.

What do you notice?
Can you explain what you've noticed?

Can you find a similar result for trapeziums in which all four lengths are whole numbers?

You might like to try More Isometric Areas next.