Regular Polygons

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?

\frac{n}{4}\csc\frac{\pi}{n}\cot\frac{\pi}{n}

\frac{n}{4}\cot\frac{\pi}{n}

\frac{n}{4}\sec\frac{\pi}{n}\tan\frac{\pi}{n}

\frac{n}{4}\tan\frac{\pi}{n}

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?

Regular Polygons - Area