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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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3 years ago
Need Help Please I'm Out Of Time ;(
vodka [1.7K]

Answer:

Total surface area = 184.86 cm²

Step-by-step explanation:

If we see the the diagram, we can find that the net of this triangular prism includes:

2 triangles each with the dimension of one side 4.3cm, second side 5.2cm and third side 6.75 cm

3 rectangles each with the dimensions of (6.75×10)cm, (5.2×10)cm and (4.3×10)cm

Surface area of triangle with a,b and c side:

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Area = 11.18cm²

For 2 triangle:

Area = 22.36cm²

Surface Area of Rectangles:

Area = (6.75×10)cm + (5.2×10)cm + (4.3×10)cm

Area = 162.5 cm²

Total surface area = area of 2 triangle + area of 3 rectangles:

Total surface area = 22.36 + 162.5

Total surface area = 184.86 cm²

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Answer:

{ \tt{g(x) = 5x - 4}}

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