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Polygon in Annulus
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 ?
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
𝑅 𝑟
𝑙
𝑅𝑟
𝑅 𝑟
𝑙
𝑅𝑟
𝑙2
𝑅𝑟
Area required
( 𝑙2 )2
+𝑟 2=𝑅2
In our case
So our area is
All the same area as this!
Note to teacher
• The regular polygons are red herrings, all that counts is the chord length, .
Resources
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
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
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
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
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
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