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Amiraneli [1.4K]
2 years ago
6

A regular hexagonal prism has an edge length 12 cm, and height 10 cm. Identify the volume of the prism to the nearest tenth.

Mathematics
1 answer:
Alexeev081 [22]2 years ago
6 0

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3

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What is <br><br> 3x+2y=-13<br> 3x+4y=1
Zepler [3.9K]

Answer:

The values are

x = -25/9 = -2 7/9

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Step-by-step explanation:

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Using eqn 2 to get the value of y

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4y/4 =( 1 -3x) / 4

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Opening the bracket

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y = 84/9 / 1/4

y = 84 * 1 / 9 *4

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y = 7/3

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y = 2 1/3

4 0
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