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Predict how many hexagons will be present if the given pattern is extended to have a total of 38 polygons.
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The word polygon simply means 2D shape.
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And we can see that our pattern contains two types of polygons.
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There are hexagons or six sided shapes.
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And there are triangles or three-sided shapes.
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And they make an alternating pattern: hexagon, triangle, hexagon, triangle, hexagon, and triangle.
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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.
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And then just count the number of hexagons that we’ve drawn.
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But there’s a quicker way to find the answer.
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Let’s have a look at that.
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Because this is a repeating pattern, we’re able to look at how the number of hexagons change as the pattern grows.
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If there were just two polygons, one of them would be a hexagon.
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When this increases to four polygons, we can see that we now have two hexagons.
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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.
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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.
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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.