### All in the Mind

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface of the water make around the cube?

### Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

### The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

# Disappearing Square

##### Stage: 3 Challenge Level:

Do you know how to find the area of a triangle?

You can count the squares.

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What happens if we turn the triangle on end? Press the button and see.

Try counting the number of units in the triangle now.

Do you have any interesting findings to report?

The area of a triangle can be found by multiplying half the base by the height. What is the area of this whole triangle?

Now find the areas of the shapes marked A, B and C.

If you add these answers together, would they equal the same as the whole triangle? Try and see.

Do you have any interesting findings to report?