Mathematics Class 9
Measuring Space: Perimeter and Area
Measure a circle's π, its arcs and sectors, and find areas from sides alone.
14 lessons · ~108 min total
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Lessons in this topic
- 0 Start here A roadmap: π and its approximations, arcs and sectors, area from sides alone, and a rectangle turned into a square. · 4 min You are here
- 1 The way round and the way across Divide the way round a circle by the way across. The answer is the same number every time. · 8 min
- 2 That number is not a fraction A fraction's decimal ends or repeats. π's decimal does neither. So no fraction equals π. · 8 min
- 3 Three approximations, each with a measured error 22/7, 3.1416 and 355/113 each miss π by a measured amount. Each is closer than the last. · 9 min
- 4 A piece of the edge An arc is the same share of the way round as its angle is of a turn. One division, one multiplication. · 8 min
- 5 Wedges, and a rectangle they approach Cut a disc into wedges and lay them in a strip. The strip gets close to a rectangle but never quite arrives. · 9 min
- 6 Checkpoint: the circle lessons A graded check on the first five ideas. · 6 min
- 7 A slice of the inside A sector's area is the same share of the circle's area as its angle is of a turn. · 8 min
- 8 An area from three sides Heron's rule finds a triangle's area from its three sides alone. No height is measured. · 9 min
- 9 Four sides on one circle Four sides on one circle fix the area. That is Brahmagupta's rule, and Heron's is the triangle case. · 9 min
- 10 A rectangle into a square A drawn construction turns a rectangle into a square of exactly the same space. · 9 min
- 11 Checkpoint: areas without heights A graded check on the sector, the three-sides rule, the vanishing side, and the square that keeps the space. · 6 min
- 12 The big picture Nine ideas on one screen: when squares cannot be counted, measure a share, a side or a semicircle. · 6 min
- 13 Track quiz A cheat-sheet table plus a reveal quiz, one question for each of the nine ideas. · 9 min
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