How many triangles will there be when the pattern is extended to have 32 polygons?
Let’s look at this pattern more closely. We can see that it begins with two triangles which are then followed by two trapeziums. The pattern then repeats: there are then two more triangles followed by two more trapeziums. The pattern will then continue in the same way.
Each time we repeat two triangles and two trapeziums. We want to know how many triangles there will be when the pattern is extended to have 32 polygons. As the repeating section of this pattern has four shapes in it, we can work out the number of repeated sections that there will be when there are 32 polygons: 32 divided by four is equal to eight.
Each repeating section of the pattern has two triangles in it. So the number of triangles will be found by multiplying eight by two. There will be 16 triangles. Another way to think about this problem is that as long as we include complete sections of the repeating pattern, then there will be the same number of triangles and trapeziums.
The number of triangles will therefore be half the total number of polygons. We know that if there are 32 polygons, then there will be eight complete sections of the pattern. We could therefore find the number of triangles by dividing the total number of polygons, 32, by two. This would give the same answer: 16 triangles.