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Refer to Problem 109 in section 6.5.
Show that the area of a regular dodecagon is given by K=3cot(π12)a2 or K=12tan(π12)r2, where a is the length of one of the sides and r is the radius of the inscribed circle.
Given that each interior angle of a regular n-sides
polygon (n≥3) measures (n−2)⋅180∘n, generalize these formulas for any such polygon.
Problem 109 in section 6.5.
Area of a Dodecagon Part I A regular dodecagon is a polygon with 12 sides of equal length. See the figure. The area of a regular dodecagon is given by the formula A=12r2tanπ12, where r is the apothem. Find the exact area of a regular dodecagon whose apothem is 10 inches.
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Chapter 7 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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