Question 19. In how many ways can the shape on the left be completely covered using nine tiles like the ones on the right? First let's take a closer look at the shape as well as the tiles. We can start off by recognizing that there are three hexagons in the shape. So we can take away two for now and just look at one. We look at different ways that we can cover it. If we place the shapes like so it is completely covered and this would be true of the other two hexagons but we are not worrying about them right now. We could also cover it in this way. Close but slightly different. Now we know that there are two ways to cover a single hexagon but there are three hexagons. So to fix this we have to do two times two times two and we get eight. So there there are eight different ways to cover the hexagons. However there will be an additional way to cover all of them when we look at them at the same time like so. So we have to add one more. When we do this we get our answer which will be D, nine.

hexagons

tiles

covering

combinations

geometry