Right pentagonal pyramid (a three-dimensional figure) has pentagon base and the apex alligned above the center of the base.- 1 base
- 10 edges
- 5 faces
- 6 vertexs
Base Area of a Right Pentagonal Pyramid formula |
||
| \( A_b \;=\; \dfrac{5}{4}\cdot tan\;54° \cdot a^2 \) | ||
| Symbol | English | Metric |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( tan \) = tangent | \( deg \) | \( rad \) |
Edge of a Right Pentagonal Pyramid formulas |
||
|
\( a \;=\; 2 \cdot \sqrt{ \dfrac {A_s ^2}{ 75 \cdot h^2 -25 \cdot \sqrt {5} \cdot h^2 + A_s \cdot \sqrt{ {200 -\;} \sqrt{8000} } } \cdot \sqrt{ {3 -\;} \sqrt {5} } } \) \( a \;=\; \left( 5 - \sqrt 5 \right) ^{1/4} \cdot \sqrt { \sqrt {10} \cdot \dfrac{A_b}{5} - \sqrt{2}\cdot \dfrac{A_b} {5} } \) \( a \;=\; \sqrt { 24 \cdot \dfrac{ V }{ 5 \cdot h \cdot \left( \sqrt 2 + \sqrt{10} \right) } } \cdot { \left( 5- \sqrt 5 \right)^{1/4} } \) |
||
| Symbol | English | Metric |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Height of a Right Pentagonal Pyramid formulas |
||
|
\( h \;=\; 24 \cdot V \cdot \dfrac { \sqrt { {5 -} \sqrt {5} } }{ 5 \cdot a^2 \cdot \left( \sqrt {2} + \sqrt {10} \right) } \) \( h \;=\; \sqrt{ \sqrt{ \dfrac{1}{500} } + \dfrac{3}{50}} \cdot \sqrt{ 6 \cdot \left(\dfrac{A_s}{a }\right)^2 - \sqrt{20} \cdot \left( \dfrac{ A_s }{ a }\right)^2 - A \cdot \sqrt{ 50 - \sqrt{500} } } \) |
||
| Symbol | English | Metric |
| \( h \) = height | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Face Area of a Right Pentagonal Pyramid formula |
||
| \( A_f \;=\; \dfrac{a}{2} \cdot \sqrt{ h^2 + \left( \dfrac{ a \cdot tan \cdot 54° }{2} \right) ^2 } \) | ||
| Symbol | English | Metric |
| \( A_f \) = face area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( tan \) = tangent | \( deg \) | \( rad \) |
Surface Area of a Right Pentagonal Pyramid formulas |
||
|
\( A_s \;=\; \dfrac{5}{2} \cdot \left( r \cdot a \right) + \dfrac{5}{2} \cdot \left( a \cdot h_s \right) \) \( V \;=\; \dfrac{5}{4} \cdot tan\;54° \cdot a^2 + 5 \cdot \dfrac{a}{2} \cdot \sqrt{ h^2 + \left( \dfrac{ a \cdot tan \cdot 54° }{ 2 } \right) ^2 } \) |
||
| Symbol | English | Metric |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h_s \) = height side | \( in \) | \( mm \) |
| \( r \) = radius | \( in \) | \( mm \) |
Volume of a Right Pentagonal Pyramid formulas |
||
|
\( V \;=\; \dfrac{5}{6} \cdot r \cdot a \cdot h \) \( V \;=\; \dfrac{5}{12} \cdot tan \; 54° \cdot a^2 \cdot h \) |
||
| Symbol | English | Metric |
| \( V \) = volume | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( tan \) = tangent | \( in \) | \( mm \) |
