Question

Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing one triangle and one square.

Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor?

Answer 1

1 square and 1 triangle because 360 – (90 + 120) = 90 + 60

2 squares because 180 = 90 + 90

1 square and 1 hexagon because 360 – (60 + 90) = 90 + 120

1 triangle and 1 hexagon because 180 = 60 + 120