Diagonal of a Right Rectangular Prism formula
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| \( D' \;=\; \sqrt{ a^2 + b^2 + h^2 } \) | ||
| Symbol | English | Metric |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
- Right rectangular prism (a three-dimensional figure) has six faces that are rectangles with equal sides and equal angles also called a right square prism.
- Diagonal is a line from one vertices to another that is non adjacent.
- 2 bases / 12 edges / 4 side faces / 8 vertexs / 4 base diagonals / 8 face diagonals / 4 space diagonal
Edge of a Right Rectangular Prism formulas |
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\( a \;=\; \dfrac{ V }{ b \cdot h } \) \( a \;=\; \sqrt{ D'^2 - h^2 - b^2 } \) \( b \;=\; \dfrac{ V }{ a \cdot h } \) \( b \;=\; \sqrt{ D'^2 - h^2 - a^2 } \) |
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| Symbol | English | Metric |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Height of a Right Rectangular Prism formulas |
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\( h \;=\; \dfrac{ V }{ a \cdot b } \) \( h \;=\; \sqrt{ D'^2 - b^2 - a^2 } \) |
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| Symbol | English | Metric |
| \( h \) = height | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Surface Area of a Right Rectangular Prism formula |
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| \( A_s \;=\; 2 \cdot \left( a \cdot b + a \cdot h + b \cdot h \right) \) | ||
| Symbol | English | Metric |
| \( A_s \) = surface area (bottom, top, sides) | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Volume of a Right Rectangular Prism formula |
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| \( V\;=\; a \cdot b \cdot h \) | ||
| Symbol | English | Metric |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |