# Being Resilient - Geometry

### Nine Colours

##### Age 11 to 16Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### Triangles to Tetrahedra

##### Age 11 to 14Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

### Estimating Angles

##### Age 7 to 14Challenge Level

How good are you at estimating angles?

### Reflecting Squarely

##### Age 11 to 14Challenge Level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

### Cuboids

##### Age 11 to 14Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

### Same Length

##### Age 11 to 16Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

### Isosceles Triangles

##### Age 11 to 14Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Kite in a Square

##### Age 14 to 18Challenge Level

Can you make sense of the three methods to work out what fraction of the total area is shaded?