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