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Regular Polygons

With equal angles and equal side lengths, what more could you want from a polygon?

Area

What is the area of a regular hexagon with side length 2?

What is the area of a regular octagon with side length 5?

Use \(\tan22.5^\circ\approx0.4,\tan67.5^\circ\approx2.4.\)

Find the area of a regular decagon whose distance from its center to a vertex is 10.

Use \(\sin18^\circ\approx0.3, \cos18^\circ\approx0.95.\)

An \(n\)-gon is a polygon with \(n\) sides. Which of the following represents the area of a regular \(n\)-gon with side length 1?

An \(n\)-gon is a polygon with \(n\) sides. Which of the following represents the area of a regular \(n\)-gon inscribed in a circle of radius 1?

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