Concept 3 of 6
The Meeting Point: Vertices
Today's big idea
A vertex is where two edges meet, and a polygon always has as many as it has sides.
A hexagon has 6 corners; a 5-point star has 10, counting its 5 inner dips too.
How it works
👀 What's going on?
A shape's corners are the places that hold it together. Count them and you can name the shape without measuring a single side.
💡 Here's the trick
Look at the hexagon above. It has 6 corners and 6 sides, and that is no coincidence. A polygon is a closed path, so every side ends exactly where the next one starts. Each corner uses up one side, which is why the two counts always match.
🪄 How to do it
- 1.Find every place where two straight edges meet, as marked on the picture above.
- 2.Count those meeting points, because each one is a vertex.
✍️ Try it
A pentagon has 5 sides, so how many vertices? Then an octagon has 8 sides, so how many vertices?
The pentagon has 5 vertices, one for each side. The octagon has 8 vertices, again one for each side. For any polygon the two counts always match.
⚠️ Watch out
A five-point star looks like it has just 5 corners, but trace right around its outline. You go out to a point, then in to a dip, then out to the next point, all the way round. That is 5 points and 5 dips, so 10 corners in all. A vertex is anywhere two edges meet, whether it juts out or folds inward.
🌟 Why this matters
Corners are where a structure is strong or weak, which is why bridges and roof frames are built out of triangles. Counting them is also the quickest way to name a shape you have never met before.
Exam tip: When a shape's name ends in -gon, the front of the word gives you the corner count.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A decagon has 10 sides. How many vertices does it have?”
- 1
What is a vertex?
A vertex is where two sides meet — a corner.
- 2
Walk around the shape
Every side ends where the next begins. Each meeting = 1 vertex.
- 3
Use the polygon rule
For any polygon: sides = vertices. 10 sides → 10 vertices.
- 4
Answer ✓
Decagon has 10 vertices
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap every corner dot of the pentagon to highlight all 5 vertices!
0 / 5 vertices found
The pentagon has 5 sides, so it has 5 VERTICES (corner points)!
Quick check
✅ VERIFICATION
How many vertices (corners) does a heptagon have?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Missing Slice
Subtract to find the missing angle.