Predict how many hexagons will be present if the given pattern is extended to have a total of 38 polygons.
The word polygon simply means 2D shape. And we can see that our pattern contains two types of polygons. There are hexagons or six sided shapes. And there are triangles or three-sided shapes. And they make an alternating pattern: hexagon, triangle, hexagon, triangle, hexagon, and triangle.
Now that we know what the pattern is, one way to find the answer could be to sketch hexagon, triangle, hexagon, triangle until we get a total of 38 polygons. And then just count the number of hexagons that we’ve drawn. But there’s a quicker way to find the answer. Let’s have a look at that.
Because this is a repeating pattern, we’re able to look at how the number of hexagons change as the pattern grows. If there were just two polygons, one of them would be a hexagon. When this increases to four polygons, we can see that we now have two hexagons. We can see that as we increase the number of shapes in the pattern, the number of hexagons is always half the total number of polygons.
So without having to draw 38 different shapes and then count up the number of hexagons, we can simply divide 38 by two to get an answer of 19. So if our given pattern is extended so there’s now a total of 38 polygons, we can predict that there will be 19 hexagons, which there are.