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
Base Area of a Right Pentagonal Prism formula |
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| \( A_b \;=\; \dfrac {1}{4} \cdot \sqrt{ 5 \cdot \left( 5 + 2 \cdot \sqrt{5} \right) \cdot a^2 } \) | ||
| Symbol | English | Metric |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
Edge of a Right Pentagonal Prism formulas |
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\( a \;=\; 25^{3/4} \cdot {\dfrac{\sqrt {A_b} }{ 5 \cdot \left( \sqrt{20} + 5 \right)^{1/4} } } \) \( a \;=\; \dfrac { - \;\left( 5 \cdot \sqrt{5} \cdot h - \sqrt{ 125 \cdot h^2 + 10 \cdot A_s \cdot \sqrt { \sqrt{500} + 25 } } \;\right) }{ 5\cdot \sqrt{ \sqrt{ 20 } + 5 } } \) \( a \;=\; \dfrac{ A_l }{ 5 \cdot h } \) |
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| Symbol | English | Metric |
| \( a \) = edge | \( in \) | \( mm \) |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( A_l \) = lateral surface area | \( in^2 \) | \( mm^2 \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
Height of a Right Pentagonal Prism formula |
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| \( h \;=\; \dfrac{A_s }{ 5 \cdot a } - \dfrac{1}{10} \cdot a \cdot \sqrt{ \sqrt{500} + 25 } \) | ||
| Symbol | English | Metric |
| \( h \) = height | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
Lateral Surface Area of a Right Pentagonal Prism formula |
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| \( A_l \;=\; 5 \cdot a \cdot h \) | ||
| Symbol | English | Metric |
| \( A_l \) = lateral surface area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Surface Area of a Right Pentagonal Prism formula |
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| \( A_s \;=\; 5 \cdot a \cdot h + \dfrac{1}{2} \cdot \sqrt{ 5\cdot \left( 5+2 \cdot \sqrt{5} \right) } \cdot a^2 \) | ||
| Symbol | English | Metric |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Volume of a Right Pentagonal Prism formula |
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| \( V \;=\; \dfrac{1}{4} \cdot \sqrt{ 5 \cdot \left ( 5+2 \cdot \sqrt{5} \right) } \cdot a^2 \cdot h \) | ||
| Symbol | English | Metric |
| \( V \) = volume | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
