Right Pentagonal Prism
Right pentagonal prism (a three-dimensional figure) has pentagonal bases and each face is a regular polygon with equal sides and equal angles.- 20 base diagonals
- 10 face diagonals
- 20 space diagonals
- 2 bases
- 15 edges
- 5 side faces
- 10 vertexs
Right Pentagonal Prism Index
- Base Area of a Right Pentagonal Prism
- Edge of a Right Pentagonal Prism
- Height of a Right Pentagonal Prism
- Lateral Surface Area of a Right Pentagonal Prism
- Surface Area of a Right Pentagonal Prism
- Volume of a Right Pentagonal Prism
Base Area of a Right Pentagonal Prism formula |
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| \(\large{ A_b= \frac {1}{4}\; \sqrt { 5 \left( 5+2\; \sqrt {5} \right) a^2 } }\) | ||
| Symbol | English | Metric |
| \(\large{ A_b }\) = base area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Edge of a Right Pentagonal Prism formulas |
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\(\large{ a = 25^{3/4} {\frac {\sqrt {A_b} } { 5\; \left( \sqrt {20}\; +5 \right) ^1/4 } } }\) \(\large{ a = \frac { - \left ( 5\; \sqrt {5} h - \sqrt { 125\;h^2 + 10\; A_s\; \sqrt { \sqrt {500}\; +25 } } \right) } { 5\; \sqrt { \sqrt { 20 }\; +5 } } }\) \(\large{ a = \frac {A_l} {5\;h} }\) |
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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 | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
Height of a Right Pentagonal Prism formula |
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| \(\large{ h = \frac {A_s} {5\;a} - \frac {1}{10}\;a\; \sqrt { \sqrt {500} +25 } }\) | ||
| Symbol | English | Metric |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_s }\) = surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
Lateral Surface Area of a Right Pentagonal Prism formula |
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| \(\large{ A_l = 5\;a\;h }\) | ||
| 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 Pentagonal Prism formula |
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| \(\large{ A_s = 5\;a\;h + \frac {1}{2} \; \sqrt { 5\; \left ( 5+2 \;\sqrt {5} \right) }\; a^2 }\) | ||
| Symbol | English | Metric |
| \(\large{ A_b }\) = base 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 Pentagonal Prism formula |
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| \(\large{ V= \frac {1}{4} \; \sqrt { 5\; \left ( 5+2\; \sqrt {5} \right) } \;a^2\;h }\) | ||
| Symbol | English | Metric |
| \(\large{ V }\) = volume | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Volume Solid Prism