Being Resilient - Geometry

Nine Colours

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?

Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

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

Estimating Angles

Age 7 to 14 Challenge Level:

How good are you at estimating angles?

Reflecting Squarely

Age 11 to 14 Challenge Level:

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

Cuboids

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?

Same Length

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?

Isosceles Triangles

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?

Kite in a Square

Age 14 to 16 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square?