Geometry — Class 3 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 3 Mathematics, Chapter 1. Naming shapes, symmetry, perimeter, tessellation and solids.
1. Shapes are named by counting
A polygon is a closed shape made only of straight lines. To name one, count its sides.
| Sides | Name | Where you see it |
|---|---|---|
| 3 | Triangle | A set square, a slice of dosai |
| 4 | Quadrilateral — square, rectangle | A book cover, a window |
| 5 | Pentagon | A home plate, some rangoli outlines |
| 6 | Hexagon | A honeycomb cell, a pencil end |
Now count the corners. A shape always has as many corners as sides. A triangle has 3 sides and 3 corners. A hexagon has 6 of each. This is worth checking on every shape you draw, because it is the fastest way to spot a mistake.
A circle is not a polygon. It has no straight sides and no corners at all.
2. Lines of symmetry
Fold a shape in half. If the two halves land exactly on top of each other, that fold line is a line of symmetry.
| Shape | Lines of symmetry |
|---|---|
| Square | 4 |
| Rectangle | 2 |
| Equilateral triangle | 3 |
| Circle | Too many to count |
Letters have symmetry too. A, M and T each have one line, straight down the middle. H has two: one down the middle and one across it.
A kolam is symmetry drawn at the doorstep every morning. The dots are placed in a grid, and the lines curl around them so that one half matches the other. Look at the next kolam you pass and try to find its fold line.
3. Perimeter is the walk around the edge
The perimeter is the total distance all the way around a shape. Add up every side.
- Square: perimeter = 4 × side
- Rectangle: perimeter = 2 × (length + breadth)
- Triangle: perimeter = side + side + side
Perimeter is measured in units of length, so the answer is in cm or m — never in square units.
4. Shapes that tile
A tessellation is a covering made of shapes that fit together with no gaps and no overlaps.
Triangles, squares, rectangles and regular hexagons all tessellate. Circles do not, because curved edges leave gaps. Regular pentagons do not either, however you turn them.
The floor tiles in your school are almost certainly squares or rectangles. A honeycomb is a hexagon tessellation that bees build without being taught.
5. Solid shapes
Flat shapes have sides and corners. Solid shapes have faces, edges and vertices.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Cylinder | 3 | 2 | 0 |
| Cone | 2 | 1 | 1 |
| Sphere | 1 | 0 | 0 |
A cube and a cuboid have the same counts. What differs is that every face of a cube is a square, while a cuboid's faces are rectangles.
6. Worked examples
Example 1. A rectangle is 8 cm long and 5 cm wide. Find its perimeter.
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm.
Example 2. A square has a side of 6 cm. Find its perimeter.
Perimeter = 4 × 6 = 24 cm.
Example 3. A triangle has sides 7 cm, 8 cm and 9 cm. Find its perimeter.
Perimeter = 7 + 8 + 9 = 24 cm.
Notice that Examples 2 and 3 both give 24 cm from completely different shapes. Perimeter tells you the distance around, and nothing about the shape itself.
Example 4. How many lines of symmetry does a rectangle have?
Two: one straight down the middle and one straight across. The diagonal is not one — fold a rectangular sheet of paper along its diagonal and the corners will not meet.
7. Practice
- How many sides and corners does a hexagon have?
- Name the polygon that has 5 sides.
- How many lines of symmetry does a square have?
- Find the perimeter of a rectangle 12 m long and 7 m wide.
- Which of these tessellate: circle, square, regular hexagon, regular pentagon?
- A rectangular playground measures 30 m by 20 m. How far does a child walk going around it twice?
- How many faces, edges and vertices does a cube have?
8. Answers
- 6 sides and 6 corners.
- Pentagon.
- Four.
- 2 × (12 + 7) = 38 m.
- Square and regular hexagon. The circle and the regular pentagon both leave gaps.
- One lap is 2 × (30 + 20) = 100 m, so two laps are 200 m.
- 6 faces, 12 edges, 8 vertices.
9. Summary
- A polygon is closed and made of straight lines; count the sides to name it, and the corners match the sides.
- A circle is not a polygon and has no corners.
- A line of symmetry is a fold that makes the halves match: square 4, rectangle 2, equilateral triangle 3.
- A rectangle's diagonal is not a line of symmetry.
- Perimeter is the distance around: 4 × side for a square, 2 × (length + breadth) for a rectangle.
- Triangles, squares, rectangles and hexagons tessellate; circles and regular pentagons do not.
- A cube has 6 faces, 12 edges and 8 vertices, and every face is a square.
