The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following
steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle.
Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.

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The Answer of The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following
steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle.
Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.

The Series of Sketches Below Starts with an Equilateral Triangle