← Measuring Space: Perimeter and Area

Lesson 12 of 14

The big picture

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When squares cannot be counted, measure something else.

Measuring Space — the chapter on one screen
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.