A flat shape with straight sides has one corner for every side
Sides and corners
A side is one straight edge of a flat shape. A corner is a point where two sides meet. A triangle has 3 sides, and 3 corners between them.
To count without a slip, start at one corner and go round the shape, touching each corner once. Stop when you are back where you began. Counting the first corner again at the end gives one too many: 4 for a triangle.
Each dot is a corner, where two sides meet. There are 3 dots, and a side runs between each pair of them.
One corner for every side
Every side runs from one corner to the next, and every corner starts the next side. So a shape with straight sides has exactly as many corners as sides. The two counts always match.
Squash a square out of shape. Its corners move, but none is added and none is taken away, so it still has 4 sides and 4 corners. Any flat shape with 4 straight sides is called a quadrilateral, however squashed it is.
Make a squashed shape with 4 sides and count its corners
Slide the number of sides, then squash the shape. The sides and the corners are numbered, and the two counts are always the same.
Five sides and six sides
A shape with 5 straight sides has 5 corners, and it is called a pentagon. A shape with 6 straight sides has 6 corners, and it is called a hexagon. Count the sides or count the corners: both give the name.
A circle is different. Its edge is one curved line with no straight sides, so it has no corners at all.
A pentagon: 5 corners, and 5 straight sides between them.
A hexagon: 6 corners, and 6 straight sides between them.
Building with shapes · The Sides and Corners of a Triangle and a Square
QuestionMei has 1 triangle and 1 square. (a) How many sides do the two shapes have in all? (b) How many corners do the two shapes have in all?
1.Count the sides of the triangle. Mark each side as you count it: 1, 2, 3. The triangle has 3 sides.
Count the sides of the triangle and mark each one: 1, 2, 3. The triangle has 3 sides. 2.Count the sides of the square in the same way: 1, 2, 3, 4. The square has 4 sides.
Count the sides of the square in the same way: 1, 2, 3, 4. The square has 4 sides. 3.(a) Add the two counts. 3 + 4 = 7. The two shapes have 7 sides in all.
(a) 3 + 4 = 7. The two shapes have 7 sides in all. 4.A corner is a point where two sides meet. Put a dot on each corner. The triangle has 3 corners and the square has 4 corners.
A corner is a point where two sides meet. The triangle has 3 corners and the square has 4 corners. 5.(b) 3 + 4 = 7. The two shapes have 7 corners in all. Each shape has as many corners as it has sides.
(b) 3 + 4 = 7. The two shapes have 7 corners in all.
Answer: (a) 7 sides; (b) 7 corners
Watch out for
- Going round the triangle and counting the first side again at the end. That gives 4 sides for a triangle. Mark each side as you count it, and stop when every side has a mark.
- Counting only the two corners at the bottom of the triangle. The point at the top is a corner too, because two sides meet there.
Building with shapes · Sticks for Two Triangles, Apart and Sharing a Side
QuestionJun builds triangles from sticks. Each side of a triangle is 1 stick. (a) How many sticks does Jun need for 2 triangles that do not touch? (b) Next Jun builds 2 triangles that share 1 side. How many sticks does he need now?
1.Build 1 triangle. It has 3 sides, so it needs 3 sticks.
Build 1 triangle. It has 3 sides, so it needs 3 sticks. 2.(a) The 2 triangles do not touch, so each one needs its own 3 sticks. 3 + 3 = 6. Jun needs 6 sticks.
(a) The 2 triangles do not touch, so each one needs its own 3 sticks. 3 + 3 = 6 sticks. 3.Now draw the 2 triangles side by side. The side in the middle belongs to both triangles. It is only 1 stick.
Now the 2 triangles are side by side. The side in the middle belongs to both triangles. It is only 1 stick. 4.(b) Count each stick once: 1, 2, 3, 4, 5. Jun needs 5 sticks. That is 6 − 1 = 5, because 1 stick is shared.
(b) Count each stick once: 1, 2, 3, 4, 5. Jun needs 5 sticks. That is 6 − 1 = 5.
Answer: (a) 6 sticks; (b) 5 sticks
Watch out for
- Writing 6 for part (b) by adding 3 + 3. That counts the shared stick two times. It is 1 stick, so it is counted once.
- Writing 4 for part (b) by taking away 1 stick for each triangle. Only 1 stick is shared, so only 1 is taken away from 6.
Your turn
1.How many corners does this shape have?