NCERT Solutions for Class 5th Maths Chapter 7 Shapes and Patterns
Updated on 2026-09-19
About this chapter
A pattern is something that repeats. In a woven mat, each strip goes over some slits and under others. Write it down in words — 1 under, 1 over, 1 under, 1 over … — and you can weave the same mat again, or tell a friend how to weave it. The rule for each row is written until it starts repeating. Tiling means covering a floor with no gaps and no overlaps. Look at the tiles in your school verandah. If copies of one shape can cover a region with no gap left over and no tile lying on top of another, we say that shape tessellates . Squares, equilateral triangles and regular hexagons tessellate. Regular pentagons and regular octagons do not. The test is at a point. Put cut-outs of the shape around one point. A full turn around a point is 360 degrees. So the corners meeting at that point must add
- Making paper mats and writing the rule for each row
- Completing the grid design
- Three regular pentagons around a point
- Which regular shapes fit around a point
- A pattern with more than one shape, and the regular octagon
- What meets at a marked point; squares and triangles together
- Cutting a rhombus into four triangles and building with them
- Angles of an equilateral triangle, and the scalene triangle
- The kite, the parallelogram and the rectangle
- Drawing on a grid, and building with 3 and 4 pieces
Quick revision
| Word | What it means | Where it appears | Example |
|---|---|---|---|
| Pattern | Something that repeats in a fixed order | Weaving Mats, page 92 | 1 under, 1 over, 1 under, 1 over … |
| Tiling | Covering a region with tiles, no gaps and no overlaps | Tiling and Tessellation, page 94 | Floor tiles in a room |
| Tessellate | To fit together with no gap and no overlap | Page 94 | Squares tessellate; regular pentagons do not |
| Regular shape | A shape with all its sides equal | Page 94 | Regular pentagon, regular hexagon |
| Pentagon / Hexagon / Octagon | A shape with 5 / 6 / 8 sides | Pages 94–95 | A regular hexagon has 6 equal sides |
| Equilateral triangle | A triangle with all three sides equal | Page 94 and Try This, page 97 | All its angles are equal too |
| Isosceles triangle | A triangle with exactly two sides equal | Page 97 | It has two equal angles |
| Scalene triangle | A triangle with no two sides equal | Page 97 | Half of an equilateral triangle |
| Rhombus | A four-sided shape with all four sides equal | Page 96 | Cut by both diagonals into 4 equal triangles |
| Kite | A quadrilateral with two pairs of equal adjacent sides | Page 98 | Side 1 = Side 2 and Side 3 = Side 4 |
| Adjacent sides | Two sides that are next to each other | Page 98 | The two upper sides of a kite |
| Parallelogram | A quadrilateral whose opposite sides are equal | Page 98 | Its opposite angles are equal |
| Rectangle | A parallelogram in which all four angles are right angles | Page 98 | A special kind of parallelogram |
| Tangram | A square cut into 7 pieces used to build shapes | Tangram, page 99 | 5 triangles, 1 square, 1 parallelogram |
| Diameter | A straight line through the centre joining two points of a circle | Play with Circles, page 101 | Two diameters give a rectangle |
| Net | A flat shape that folds up into a solid | Cube Connections, page 102 | The cross-shaped net of a cube |
| Face / Edge / Vertex | A flat surface / a line where two faces meet / a corner point | Pages 102–103 | A cube has 6 faces |
| Icosahedron | A solid with 20 equal triangular faces | Page 103 | Icosa means twenty |
| Dodecahedron | A solid with 12 equal pentagonal faces | Page 103 | Dodeca means twelve |
Exercises
- Making paper mats and writing the rule for each row — Weaving Mats Page 92–93
- Completing the grid design — Let Us Try Page 93
- Three regular pentagons around a point — Tiling and Tessellation Page 94
- Which regular shapes fit around a point — Find Out Page 94
- A pattern with more than one shape, and the regular octagon — Tiling and Tessellation Page 95
- What meets at a marked point; squares and triangles together — Tiling and Tessellation Page 96
- Cutting a rhombus into four triangles and building with them — Shapes from the Rhombus Page 96–97
- Angles of an equilateral triangle, and the scalene triangle — Try This Page 97
- The kite, the parallelogram and the rectangle — Shapes from the Rhombus Page 98
- Drawing on a grid, and building with 3 and 4 pieces — Shapes from the Rhombus Page 99
- Naming the seven pieces and building shapes with them — Tangram Page 99
- Matching statements with the square, rectangle, rhombus and parallelogram — Which Shape Am I? Page 100
- Folding a square sheet into a kite — Kites Page 100
- Two diameters and the shape they make — Play with Circles Page 101
- Stitching a design on 24 points, and the flower of circles — Circle Designs Page 101
- Views and nets, hollow cube frames, and Nisha's painted cube — Cube Connections Page 102
- Tanu's row of seven shapes — Puzzle Page 102
- Counting faces, vertices and edges of two beautiful solids — Icosahedron and Dodecahedron Page 103