The Area of Annulus Enclosed by Circles and Regular Polygons
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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Presentation Transcript
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 ? 2 2
? ? ? ? ?
Area required = ??2 ??2 = ? ?2 ?2 2 ? 2 = ? ? ? In our case ? = 2 So our area is ? ? ? ? ? ? 2 ? 2 ? 2 + ?2= ?2
Note to teacher The regular polygons are red herrings, all that counts is the chord length, ?.
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
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
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
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
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
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
