Question

The area of a polygon of n sides inscribed in a circle of radius r is

Answer 1

\[A=\frac{ nr^2 }{ 2}\sin(\frac{ 2\pi }{ n })\]

Answer 2

If r=12 what is the limit of A as n approaches infinity?

Answer 3

@Michele_Laino

Answer 4

452.39

658.02

37.70

226.19

Answer 5

Thing about this one

Answer 6

we can rewrite your formula as below:
\[\Large \frac{{n{r^2}}}{2}\sin \left( {\frac{{2\pi }}{n}} \right) = \frac{{n{r^2}}}{2} \times \left( {\frac{{2\pi }}{n}} \right) \times \frac{{\sin \left( {\frac{{2\pi }}{n}} \right)}}{{\left( {\frac{{2\pi }}{n}} \right)}}\]

Answer 7

now, we have to keep in mind that:
\[\mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{x} = 0\]

Answer 8

so, what do you get?

Answer 9

hold up Im right all this down

Answer 10

Im getting an error

Answer 11

I put in like this http://www.wolframalpha.com/input/?i=nr^2%2F2x%282%283.14%29%2Fn%29xsin%282%283.14%29%2Fn%29%2F%282%283.14%29%2Fn%29

Answer 12

hint:
\[\Large \begin{gathered}
\frac{{n{r^2}}}{2} \times \left( {\frac{{2\pi }}{n}} \right) \times \frac{{\sin \left( {\frac{{2\pi }}{n}} \right)}}{{\left( {\frac{{2\pi }}{n}} \right)}} = \frac{{n{r^2}2\pi }}{{2n}} \times \frac{{\sin \left( {\frac{{2\pi }}{n}} \right)}}{{\left( {\frac{{2\pi }}{n}} \right)}} \hfill \\
\hfill \\
= \pi {r^2} \times \frac{{\sin \left( {\frac{{2\pi }}{n}} \right)}}{{\left( {\frac{{2\pi }}{n}} \right)}} \hfill \\
\end{gathered} \]

Answer 13

3.14r^2x(sin)(2(3.14)/n)/2(3.14)/n

Answer 14

http://www.wolframalpha.com/input/?i=3.14r^2x%28sin%29%282%283.14%29%2Fn%29%2F2%283.14%29%2Fn

Answer 15

I cant get the text command for that

Answer 16

I keep getting errors every way I put it in

Answer 17

its a error or none of the answers

Answer 18

hint:
when n goes to infinity, then:
(2 pi/n) goes to zero, so we can write:
\[\Large \mathop {\lim }\limits_{x \to 0} \frac{{\sin \left( {\frac{{2\pi }}{n}} \right)}}{{\left( {\frac{{2\pi }}{n}} \right)}} = 1\]
sorry, I have made an error, the right formula, is:
\[\mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{x} = 1\]

Answer 19

is it 452.39

Answer 20

that's right!