Right Hexagonal Prism
Right hexagon prism (a three-dimensional figure) is where each face is a regular polygon with equal sides and equal angles.- Long diagonal always crosses the center point of the hexagon.
- Short diagonal does not cross the center point of the hexagon.
- 36 base diagonals
- 12 face diagonals
- 36 space diagonals
- 2 bases
- 18 edges
- 6 side faces
- 12 vertexs
Base Area of a Right Hexagonal Prism formula |
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| \(\large{ A_b = 3\; \sqrt {3}\; \frac { a^2 } { 2 } }\) | ||
| Symbol | English | Metric |
| \(\large{A_b }\) = base area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Base Long Diagonal of a Right Hexagon formula |
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| \(\large{ D_l = 2\;a }\) | ||
| Symbol | English | Metric |
| \(\large{ D_l }\) = long diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Base Short Diagonal of a Right Hexagon formula |
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| \(\large{ D_s = \sqrt{3}\;a }\) | ||
| Symbol | English | Metric |
| \(\large{ D_s }\) = short diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Side Diagonal of a Right Hexagonal Prism formula |
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| \( \large{ d' = \sqrt { a^2 + h^2 } }\) | ||
| Symbol | English | Metric |
| \(\large{ d' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Edge of a Right Hexagonal Prism formulas |
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\(\large{ a = \frac { A_{l} } { 6\;h } }\) \(\large{ a = 3^{1/4}\; \sqrt {2\; \frac { V } { 9\;h } } }\) \(\large{ a = \frac{1}{3} \; \sqrt { 3\;h^2 + \sqrt {3}\; A_s } - \sqrt {3}\; \frac {h}{3} }\) \(\large{ a = 3^{1/4}\; \sqrt {2\; \frac { A_b } { 9 } } }\) |
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| Symbol | English | Metric |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_b }\) = base area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_l }\) = lateral surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ A_s }\) = surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
Height of a Right Hexagonal Prism formulas |
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\(\large{ h = 2\; \sqrt {3}\; \frac { V } { 9\;a^2 } }\) \(\large{ h = \frac {A_s} {6\;a } - \sqrt {3}\; \frac { a } {2 } }\) |
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| Symbol | English | Metric |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_s }\) = surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
Lateral Surface Area of a Right Hexagonal Prism formula |
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| \(\large{ A_l = 6\;a\;h }\) | ||
| Symbol | English | Metric |
| \(\large{ A_l }\) = lateral surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Surface Area of a Right Hexagonal Prism formula |
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| \(\large{ A_s = 6\;a\;h + 3\; \sqrt 3\; a^2 }\) | ||
| Symbol | English | Metric |
| \(\large{ A_s }\) = surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Volume of a Right Hexagonal Prism formulas |
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\(\large{ V = \frac{3\; \sqrt {3} }{ 2 } \; a^2\;h }\) \(\large{ V = 3 \; a \; b \; h }\) |
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| Symbol | English | Metric |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ b }\) = center | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Volume Equations