Question 3 - Figure it out - Page 72 - Chapter 4 Class 8 - Exploring Some Geometric Themes (Ganita Prakash II

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Question 3 Find the area of the region remaining at the nth step in each of the shape sequences that lead to the Sierpinski fractals. Take the area of the starting square/triangle to be 1 sq. unit.Let’s do for both Sierpinski Carpet At each step, you take a shape, cut it into 9 equal pieces, and remove 1 . This means you are keeping 8/9 of the area. Step 0 Area: 1 Step 1 Area: 𝟏×𝟖/𝟗 Step 2 Area: 8/9×8/9=(𝟖/𝟗)^𝟐 Step 𝒏 Area: (𝟖/𝟗)^𝒏 Sierpinski Gasket At each step, you take a triangle, cut it into 4 equal pieces, and remove 1 . This means you are keeping 3/4 of the area. Step 0 Area: 1 Step 1 Area: 𝟏×𝟑/𝟒 Step 2 Area: 3/4×3/4=(𝟑/𝟒)^𝟐 Step 𝒏 Area: (𝟑/𝟒)^𝒏