NCERT Solutions for Class 6th Maths Chapter 6 Perimeter and Area
Updated on 2026-09-19
About this chapter
The perimeter of a closed plane figure is the distance you cover going once around its boundary. For a polygon it is simply the sum of the lengths of all its sides . Perimeter of a rectangle = 2 × (length + breadth) , perimeter of a square = 4 × side , and for any regular polygon, perimeter = number of sides × length of a side . The area of a closed figure is the amount of region it encloses. It is measured in square units — sq cm, sq m, square units of a grid. Area of a rectangle = length × width and area of a square = side × side . Squares are used as the unit of area because they pack together with no gaps and no overlaps. The area of an irregular shape is estimated by counting squares on graph paper: a full square counts 1, more than half counts 1, exactly half counts ½, less than half
- Perimeter
- Matha Pachchi!
- Deep Dive · Estimate and Verify
- Straight and diagonal units · Perimeter of a regular polygon
- Regular polygons · Split and rejoin
- Area
- The tangram pieces
- Estimating area by counting squares
- Why squares? · Rectangles of a given area
- Area of a Triangle
Quick revision
| Idea | Formula / rule | Worked example from the chapter | Units |
|---|---|---|---|
| Perimeter of a polygon | Sum of the lengths of all sides | 4 cm + 5 cm + 7 cm = 16 cm | cm, m |
| Perimeter of a rectangle | 2 × (length + breadth) | 2 × (12 + 8) = 40 cm | cm, m |
| Perimeter of a square | 4 × side | 4 × 1 m = 4 m | cm, m |
| Perimeter of an equilateral triangle | 3 × side | 3 × 5 cm = 15 cm | cm, m |
| Perimeter of a regular polygon | Number of sides × side | Regular hexagon: 6 × 6 cm = 36 cm | cm, m |
| Area of a rectangle | length × width | 5 m × 4 m = 20 sq m | sq cm, sq m |
| Area of a square | side × side | 3 m × 3 m = 9 sq m | sq cm, sq m |
| Area by counting squares | full = 1, more than half = 1, half = ½, less than half = 0 | The four dot-grid figures give 4, 9, 10 and 11 sq units | square units |
| Triangle inside a rectangle | Half the area of the rectangle | Triangle BAD = ½ × 20 = 10 sq units | square units |
| Splitting a figure | Cut it into rectangles and triangles, then add | Staircase figure = 9 + 7 + 10 + 2 = 28 sq m | sq m |
| Same area, different perimeter | 9 unit squares → perimeter 12, 18 or 20 units | 3 × 3 square is 12; 1 × 9 strip is 20 | units |
| Same area, least perimeter | The rectangle closest to a square | Area 24: 4 × 6 has the least perimeter, 20 units | units |
Exercises
- Figure it Out — Perimeter Page 132
- Matha Pachchi! — Figure it Out Page 133
- Deep Dive · Estimate and Verify — In-text Questions Page 134
- Straight and diagonal units · Perimeter of a regular polygon — In-text Questions Page 135
- Regular polygons · Split and rejoin — In-text Questions Page 136
- In-text Question — Area Page 137
- Figure it Out — Area Page 138
- The tangram pieces — Figure it Out Page 139
- Estimating area by counting squares — In-text Questions Page 140
- Why squares? · Rectangles of a given area — Let’s Explore Page 141 & 142
- In-text Questions — Area of a Triangle Page 142
- Areas of triangles on grid paper — In-text Questions Page 143 & 144
- Areas by splitting into rectangles and triangles — Figure it Out Page 144
- Making it ‘More’ or ‘Less’ — In-text Questions Page 145 & 146
- Charan’s house plan — In-text Questions Page 146
- Sharan’s house plan — In-text Questions Page 147
- Finding a missing length or a missing area — Area Maze Puzzles Page 148
- Figure it Out — mixed practice on perimeter and area Page 149