circles, polygons, circumference and perimeter what can you deduce, given very little information?
TRANSCRIPT
![Page 1: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/1.jpg)
Circles, Polygons, Circumference and PerimeterWHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?
![Page 2: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/2.jpg)
The circle has a diameter of 1 unit.
1
![Page 3: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/3.jpg)
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
![Page 4: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/4.jpg)
What is the perimeter of the circumscribed square?
![Page 5: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/5.jpg)
What is the perimeter of the inscribed regular hexagon?
![Page 6: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/6.jpg)
What is the circumference of the circle?
![Page 7: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/7.jpg)
What can you say about the perimeter of this regular inscribed octagon?
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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?
![Page 9: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/9.jpg)
What would be the greatest length of the perimeter of an inscribed regular polygon, however many sides it has?
![Page 10: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/10.jpg)
GeneralisingUSING SYMBOLS
![Page 11: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/11.jpg)
The circle has a diameter d.
d
![Page 12: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/12.jpg)
The circle has a diameter d.
This is the only piece of information you will be given.
d
![Page 13: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/13.jpg)
What is the perimeter of the circumscribed square?
![Page 14: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/14.jpg)
What is the perimeter of the inscribed regular hexagon?
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What is the circumference of the circle?
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Extension questionsHIGHER TIER
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Is the perimeter of the semicircle half the circumference of the circle?
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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?
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This time, the circle has a radius of 1 unit.
1
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What is the perimeter of the inscribed equilateral triangle?
![Page 21: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/21.jpg)
Some hintsADDING USEFUL LINES!
![Page 22: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/22.jpg)
What is the perimeter of the inscribed regular hexagon?
![Page 23: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/23.jpg)
What is the perimeter of the inscribed regular hexagon?
We could add the diameter …
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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?
![Page 25: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/25.jpg)
What is the perimeter of the inscribed equilateral triangle?
![Page 26: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/26.jpg)
What is the perimeter of the inscribed equilateral triangle?
The radius of the circle may help …
![Page 27: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/27.jpg)
… especially if we draw 3 of them …
![Page 28: Circles, Polygons, Circumference and Perimeter WHAT CAN YOU DEDUCE, GIVEN VERY LITTLE INFORMATION?](https://reader035.vdocuments.site/reader035/viewer/2022070414/5697c00b1a28abf838cc8138/html5/thumbnails/28.jpg)
… and project the lines …… to create other triangles whose angles we can deduce …… and whose side lengths we can calculate.