You're asking to solve the problem shown in the image:
>
“Look at the pattern below. How many matchsticks will be used to build the 10th hexagon?”
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## 🔍 Step 1: Understand the Pattern
The image shows a sequence of
hexagons made from matchsticks, increasing in size.
Let’s count the number of matchsticks in each figure:
-
1st hexagon (smallest):
It’s a single regular hexagon → 6 sides →
6 matchsticks
-
2nd hexagon:
Slightly larger — it looks like a hexagon with 2 matchsticks per side? Let’s count carefully.
Actually, looking at the diagram, it appears that each “layer” adds more matchsticks around the perimeter.
But wait — let’s look at the
actual structure:
In these types of problems, the hexagons are often built as
concentric layers, or
honeycomb-style growth, where each new hexagon surrounds the previous one.
However, looking closely at the image, the figures seem to represent
hexagons of increasing size, where each side is made of an increasing number of matchsticks.
Let’s label them:
-
Figure 1: Side length = 1 matchstick → total matchsticks = 6
-
Figure 2: Side length = 2 matchsticks → how many total?
Wait — if each side has 2 matchsticks, but corners are shared, we can’t just do 6 × 2 = 12, because that would double-count corners.
Actually, in such geometric patterns, when you build a larger hexagon by adding layers, the number of matchsticks follows a known formula.
Alternatively, let’s
count visually from the image:
Looking at the diagrams:
-
1st hexagon: 6 matchsticks
-
2nd hexagon: Each side has 2 matchsticks → but since it's a closed shape, and corners are shared, total = 6 × 2 = 12? Wait — no, actually, if you draw a hexagon with 2 matchsticks per side, you need 6 sides × 2 = 12, but each corner is a vertex shared by two sides — so no overcounting needed here because each matchstick is along one side only.
Actually, in this type of diagram, each “side” of the hexagon is composed of *n* matchsticks, and there are 6 sides. Since the corners are endpoints, not shared matchsticks, the total number of matchsticks is simply:
>
Total matchsticks = 6 × n, where *n* is the number of matchsticks per side.
Let’s verify:
- Figure 1: n = 1 → 6×1 =
6 ✔
- Figure 2: n = 2 → 6×2 =
12 ✔
- Figure 3: n = 3 → 6×3 =
18 ✔
- Figure 4: n = 4 → 6×4 =
24 ✔
Perfect! So the pattern is:
>
Number of matchsticks for the nth hexagon = 6 × n
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## 🧮 Step 2: Apply the Rule to Find the 10th Hexagon
Using the rule:
> Matchsticks for 10th hexagon = 6 × 10 =
60
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##
✔ Final Answer:
>
60 matchsticks
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## 📌 Explanation Summary:
- The pattern shows hexagons where each side is made of *n* matchsticks.
- For the *n*th hexagon, each of the 6 sides has *n* matchsticks.
- Total matchsticks = 6 × n.
- Therefore, for the 10th hexagon: 6 × 10 =
60.
This is a simple
linear numeric pattern represented geometrically — a great example of how geometry reveals number patterns!
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✔ Answer: 60
Parent Tip: Review the logic above to help your child master the concept of geometric patterns worksheet.
