Hinglish

Patterns in Shapes

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.5

Learn

Patterns are not only in numbers. Shapes can grow by a rule too. The part of maths that studies shapes is called geometry. Here are some shape sequences.

Regular polygons: triangle, quadrilateral, pentagon, hexagon, then heptagon, octagon, nonagon, decagon … 'Regular' means all sides are the same length and all corners look the same.

Complete graphs: put some points and join every point to every other point. K2 has 2 points, K3 has 3, K4 has 4 …

Stacked squares: a big square cut into smaller equal squares: 1, then 2 by 2, then 3 by 3 …

Stacked triangles: a big triangle cut into small equal triangles, with one more row each time.

Koch snowflake: start with a triangle. At each step, every straight line gets a 'speed bump' in its middle. The changes get tinier and tinier.

Explore: make regular polygons and complete graphs. Watch how the sides and lines grow.

  1. Make a hexagon.
  2. Make the polygon with 8 sides. What is it called?
  3. Join points (each to every other) so that there are exactly 10 lines.

Remember

  • Geometry is the part of maths that studies shapes.
  • Shape sequences: regular polygons, complete graphs, stacked squares, stacked triangles, Koch snowflake.

Quick check

In the Regular Polygons sequence, which shape comes after the hexagon?

  1. Pentagon
  2. Heptagon
  3. Octagon
  4. Decagon
Answer

Heptagon. Hexagon has 6 sides, so the next one has 7 sides: the heptagon.

Think about it

A shape sequence goes: triangle, square, pentagon, … What is the 7th shape, and how many sides does it have?

One answer

Each shape has one more side than the one before, starting with 3. The 7th shape has 3 + 6 = 9 sides: a nonagon.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.