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# Being Resilient - Geometry

### Nine Colours

### Triangles to Tetrahedra

### Reflecting Squarely

### Cuboids

### Same Length

### Isosceles Triangles

### Kite in a Square

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Age 11 to 16

Challenge 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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge 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?

Age 11 to 16

Challenge Level

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

Age 11 to 14

Challenge 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?

Age 14 to 18

Challenge Level

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