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Polygon in Annulus
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Polygon in Annulus
You have two figures that each show a regular polygon (with a given side length) just touching two circles.
What is the area of the annulus, i.e. the area enclosed by the circles, in terms of ?
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Each figure shows a regular polygon (with a given side length) just touching two circles.
What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
22
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𝑅 𝑟
𝑙
𝑅𝑟
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𝑅 𝑟
𝑙
𝑅𝑟
𝑙2
𝑅𝑟
Area required
( 𝑙2 )2
+𝑟 2=𝑅2
In our case
So our area is
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All the same area as this!
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Note to teacher
• The regular polygons are red herrings, all that counts is the chord length, .
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Resources
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Each figure shows a regular polygon (with a given side length) just touching two circles.
What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
22SIC_18
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What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
Each figure shows a regular polygon (with a given side length) just touching two circles.
22SIC_18
![Page 18: Polygon in Annulus. You have two figures that each show a regular polygon (with a given side length) just touching two circles. What is the area of the](https://reader036.vdocuments.net/reader036/viewer/2022062301/56649f435503460f94c63e29/html5/thumbnails/18.jpg)
What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
Each figure shows a regular polygon (with a given side length) just touching two circles.
2 2SIC_18
![Page 19: Polygon in Annulus. You have two figures that each show a regular polygon (with a given side length) just touching two circles. What is the area of the](https://reader036.vdocuments.net/reader036/viewer/2022062301/56649f435503460f94c63e29/html5/thumbnails/19.jpg)
What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
Each figure shows a regular polygon (with a given side length) just touching two circles.
2 2SIC_18
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What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
Each figure shows a regular polygon (with a given side length) just touching two circles.
2 2SIC_18
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What is the area of each annulus, i.e. the area enclosed by the circles, in terms of ?
Each figure shows a regular polygon (with a given side length) just touching two circles.
22
SIC_18