35. Find the probability that the measure of an interior angle of a regular n-gon is a positive integer when n is an integer and 3 <_ n <_ 12

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amulets5239

31.08.2022

Mathematics

Are of shaded region = area of circle - area of segment
$= \pi {r}^{2} - ((\alpha \div 360) \times \pi \times {r}^{2} )$
$= \pi {r}^{2} (1 - \alpha \div 360)$
$r = 8.35 \\ \alpha = 100$
= 158.1666....

$rounding \: up$
$area \: of \: shaded \: region \: = 158.2 \: \: square ft$

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