Being Resilient - Geometry
Nine Colours
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
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Reflecting Squarely
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Cuboids
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
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Isosceles Triangles
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
Can you make sense of the three methods to work out what fraction of the total area is shaded?