Understanding the Area of Annulus Enclosed by Circles and Regular Polygons

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Explore how the area of an annulus, enclosed by circles and regular polygons with a given side length, is calculated. The focus is on chord length (?), rather than regular polygon details, to determine the area. Follow the step-by-step explanation and visual aids provided to grasp this geometric concept effectively.


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  1. Polygon in Annulus

  2. 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 ?

  3. 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 ? 2 2

  4. ? ? ? ? ?

  5. Area required = ??2 ??2 = ? ?2 ?2 2 ? 2 = ? ? ? In our case ? = 2 So our area is ? ? ? ? ? ? 2 ? 2 ? 2 + ?2= ?2

  6. All the same area as this!

  7. Note to teacher The regular polygons are red herrings, all that counts is the chord length, ?.

  8. Resources

  9. 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 ? 2 2 SIC_18

  10. 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 ? 2 SIC_18 2

  11. 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 ? 2 SIC_18 2

  12. 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 ? 2 2 SIC_18

  13. 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 ? 2 2 SIC_18

  14. 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 ? 2 2 SIC_18

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