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###### Let's investigate a curve that has an infinite length yet having finite area: Consider a sequence of curves generated by starting with an equilateral triangle whose side has a length of 1 (stage 1} Successive stages (stages 2,3,4,-progress by:Stepl: Divide each side into three equal partsStep2: Draw an equilateral triangle on each middle part:Step3: Divide each outer side into thirds_Step4: Draw an equilateral triangle on each middle part(a) Find the length Ln of the n-th stage(b) Show that

Let's investigate a curve that has an infinite length yet having finite area: Consider a sequence of curves generated by starting with an equilateral triangle whose side has a length of 1 (stage 1} Successive stages (stages 2,3,4,-progress by: Stepl: Divide each side into three equal parts Step2: Draw an equilateral triangle on each middle part: Step3: Divide each outer side into thirds_ Step4: Draw an equilateral triangle on each middle part (a) Find the length Ln of the n-th stage (b) Show that lim Lr (c) Find the area Aof the n-th stage Show that lim An 8/5) A1 where Az is the area of the figure in stage 1 Stage Stage 2 Stare 6x 5tage Stage

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