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What is the area of a regular n-gon with side length s and apothem a?
Hint: Break the polygon up into n congruent triangles.
What is the angle θ made between two consecutive sides of a regular n-gon?
Hint: Use the same triangles that were used to compute the area.
What is the radius r in terms of s?
Hint: Use the law of sines.
What is the length a of the apothem in terms of s?
Hint: Use the Pythagorean theorem.
Hint: First find θk, the angle between a side and the (k – 1)th diagonal in the triangles below. Then use the law of sines.
How many diagonals does an n-gon have?
Hint: In how many ways can we choose two distinct vertices?