Base Area of a Right Hexagonal Prism formula |
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| \( A_b \;=\; 3 \cdot \sqrt{3} \cdot \dfrac{ a^2 }{ 2 } \) | ||
| Symbol | English | Metric |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
- 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 vertex
Base Long Diagonal of a Right Hexagon formula
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| \( D_l \;=\; 2 \cdot a \) | ||
| Symbol | English | Metric |
| \( D_l \) = long diagonal | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
Base Short Diagonal of a Right Hexagon formula
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| \( D_s \;=\; \sqrt{3} \cdot a \) | ||
| Symbol | English | Metric |
| \( D_s \) = short diagonal | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
Side Diagonal of a Right Hexagonal Prism formula |
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| \( d' \;=\; \sqrt{ a^2 + h^2 } \) | ||
| Symbol | English | Metric |
| \( d' \) = diagonal | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Edge of a Right Hexagonal Prism formulas |
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\( a \;=\; \dfrac{ A_l }{ 6 \cdot h } \) \( a \;=\; 3^{1/4} \cdot \sqrt{ 2 \cdot \dfrac{ V }{ 9 \cdot h } } \) \( a \;=\; \dfrac{1}{3} \cdot \sqrt{ 3 \cdot h^2 + \sqrt{3} \cdot A_s } - \sqrt{3} \cdot \dfrac {h}{3} \) \( a \;=\; 3^{1/4} \cdot \sqrt{2 \cdot \dfrac{ A_b }{ 9 } } \) |
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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 | \( in^2 \) | \( mm^2 \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Height of a Right Hexagonal Prism formulas |
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\( h \;=\; 2 \cdot \sqrt{ 3 } \cdot \dfrac{ V }{ 9 \cdot a^2 } \) \( h \;=\; \dfrac{ A_s }{ 6 \cdot a } - \sqrt{ 3 } \cdot \dfrac{ a }{ 2 } \) |
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| Symbol | English | Metric |
| \( h \) = height | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Lateral Surface Area of a Right Hexagonal Prism formula |
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| \( A_l \;=\; 6 \cdot a \cdot h \) | ||
| 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 Hexagonal Prism formula |
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| \( A_s \;=\; 6 \cdot a \cdot h + 3 \cdot \sqrt{ 3 } \cdot a^2 \) | ||
| Symbol | English | Metric |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Volume of a Right Hexagonal Prism formulas |
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\( V \;=\; \dfrac{ 3 \cdot \sqrt{ 3 } }{ 2 } \cdot a^2 \cdot h \) \( V \;=\; 3 \cdot a \cdot b \cdot h \) |
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| Symbol | English | Metric |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
| \( b \) = center | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |