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Svetllana [295]
3 years ago
14

The area of a regular octagon is 35 cm^2. What is the area of a regular octagon with sides five times as long?

Mathematics
1 answer:
Marat540 [252]3 years ago
3 0
So... let's say the smaller regular octagon has sides of "x" long, then the larger octagon will have sides of 5x.

\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\

\bf \cfrac{small}{large}\quad \stackrel{area~ratio}{\cfrac{s^2}{s^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{(5x)^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{5^2x^2}}\implies \stackrel{area~ratio}{\cfrac{\underline{x^2}}{25\underline{x^2}}}=\stackrel{area~ratio}{\cfrac{35}{a}}
\\\\\\
\cfrac{1}{25}=\cfrac{35}{a}\implies a=\cfrac{25\cdot 35}{1}
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Answer:

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It should look like this:

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49 x 2. Multiply 49 x 2, and your answer should be 98.

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an exponential function to model the quail population:

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<h3>Volume of composite object</h3>

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V = 4/3πr³

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<u>For the outer sphere:</u>

V = 4/3π(20)³

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The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

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