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(Solved): The following diagram shows a series of nested equilateral triangles. These triangles are shaded in ...
The following diagram shows a series of nested equilateral triangles. These triangles are shaded in black. The outer triangle has sides of
20cm. Triangles continue to be inscribed ad infinitum, each with a side length half the previous. a. Determine the area of the first nested triangle. You may want to use the fact that the area of an equilateral triangle is given by
(\sqrt(3))/(4)\times base^(2). Leave your answer in exact form. b. Write down the sequence that gives the areas of the first three triangles. Leave your answers in exact form. (Be careful - if you halve the length of each side by what fraction does area decrease?) c. Determine the area of the first 10 nested triangles
