(a) Let $ A_n $ be the area of a polygon with $ n $ equal sides inscribed in a circle with radius $ r $. By dividing the polygon into $ n $ congruent triangles with central angle $ 2\pi/n $, show that

$$ A_n = \frac{1}{2} nr^2 \sin \biggl( \frac{2 \pi}{n} \biggr) $$

(b) Show that $ \displaystyle \lim_{n \to \infty} A_n = \pi r^2 $. [$ Hint: $ Use Equation 3.3.2 on page 191.]

## Discussion

## Video Transcript

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