Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
An interactive activity for one to experiment with a tricky tessellation
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with $15$ copies of itself, be used to cover an eight by eight chessboard?
What about the other four tetrominoes?
If the set of tetrominoes can fill the board sketch a solution showing how this can be done and if it is impossible to cover the board then explain why.