The big picture
When squares cannot be counted, measure something else.
| Idea | Remember | Example |
|---|---|---|
| Way round ÷ way across | One number for every circle. | 44 ÷ 14 = 22/7 |
| Not a fraction | π's decimal never ends or repeats. | 22/7 and π differ |
| Three misses | Each is closer than the last. | 0.00126, 0.0000073, 0.00000027 |
| The arc | An arc is a share of the way round. The share is the angle's share of a turn. | 44 × 90/360 = 11 |
| The circle's area | The strip is half the way round long. It is the radius wide. | 22 × 7 = 154 |
| The sector | A sector's area is a share of the circle's area. The share is the angle's share of a turn. | 154 × 90/360 = 38.5 |
| Heron | Half the perimeter. Take each side from it. Multiply the four numbers. Then find the number that squares to the product. | 13, 14, 15 gives 84 |
| Brahmagupta | Half the perimeter. Take each of the four sides from it. Multiply the four brackets. Then find the number that squares to the product. | 3, 4, 5, 6 gives √360 |
| Rectangle into square | Carry the width past the long side. Swing a semicircle on the whole length. Raise a perpendicular where the long side ends. That length is the square's side. | 9 × 4 gives a side of 6 |
Open Chapter 6, Measuring Space: Perimeter and Area, in your NCERT book.