Answer:
the area of the hexagon is approx. 187.1 in²
Step-by-step explanation:
Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in. We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.
One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°. The height of one such triangle is
h = (12 in)sin 60°, or
√3
h = (12 in) -------- = 6√3 in
2
So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is
A = (1/2)(12 in)(6√3 in) = 36√3 in²
and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²
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so as you can see the common ratio is 2, and the first term is 1/2,
![\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bsum%20of%20a%20finite%20geometric%20sequence%7D%20%5C%5C%5C%5C%20S_n%3D%5Csum%5Climits_%7Bi%3D1%7D%5E%7Bn%7D%5C%20a_1%5Ccdot%20r%5E%7Bi-1%7D%5Cimplies%20S_n%3Da_1%5Cleft%28%20%5Ccfrac%7B1-r%5En%7D%7B1-r%7D%20%5Cright%29%5Cquad%20%20%5Cbegin%7Bcases%7D%20n%3Dn%5E%7Bth%7D%5C%20term%5C%5C%20a_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%20r%3D%5Ctextit%7Bcommon%20ratio%7D%5C%5C%20----------%5C%5C%20r%3D2%5C%5C%20a_1%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%20n%3D8%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20S_8%3D%5Ccfrac%7B1%7D%7B2%7D%5Cleft%28%20%5Ccfrac%7B1-2%5E8%7D%7B1-2%7D%20%5Cright%29%5Cimplies%20S_8%3D%5Ccfrac%7B1%7D%7B2%7D%5Cleft%28%20%5Ccfrac%7B-255%7D%7B-1%7D%20%5Cright%29%5Cimplies%20S_8%3D%5Ccfrac%7B255%7D%7B2%7D%20)
Answer:
3/8 pages per minute
Step-by-step explanation:
Divide 3/4 by 2 by multiplying by reciprocal: 3/4 * 1/2 = 3/8
No, line graphs are used only to show change over time