circles, polygons, circumference and perimeter what can you deduce, given very little information?
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Circles, Polygons, Circumference and PerimeterWHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?
The circle has a diameter of 1 unit.
1
The circle has a diameter of 1 unit.
This is the only piece of information you will be given, other than explanations of mathematical vocabulary.
1
What is the perimeter of the circumscribed square?
What is the perimeter of the inscribed regular hexagon?
What is the circumference of the circle?
What can you say about the perimeter of this regular inscribed octagon?
What can you say about the perimeter of the regular octagon, compared to the regular hexagon?
Would you expect the perimeter of a regular, inscribed decagon to be greater or less than that of the octagon?
What would be the greatest length of the perimeter of an inscribed regular polygon, however many sides it has?
GeneralisingUSING SYMBOLS
The circle has a diameter d.
d
The circle has a diameter d.
This is the only piece of information you will be given.
d
What is the perimeter of the circumscribed square?
What is the perimeter of the inscribed regular hexagon?
What is the circumference of the circle?
Extension questionsHIGHER TIER
Is the perimeter of the semicircle half the circumference of the circle?
What is the perimeter of the inscribed square,
a) if the diameter of the circle is 1?
b) if the diameter of the circle is d?
This time, the circle has a radius of 1 unit.
1
What is the perimeter of the inscribed equilateral triangle?
Some hintsADDING USEFUL LINES!
What is the perimeter of the inscribed regular hexagon?
What is the perimeter of the inscribed regular hexagon?
We could add the diameter …
What is the perimeter of the inscribed regular hexagon?
… but these are also diameters.
What triangles are these? How do you know?
What are the lengths of their sides?
What is the perimeter of the inscribed equilateral triangle?
What is the perimeter of the inscribed equilateral triangle?
The radius of the circle may help …
… especially if we draw 3 of them …
… and project the lines …… to create other triangles whose angles we can deduce …… and whose side lengths we can calculate.