Right square prism (a three-dimensional figure) has square bases, four faces that are rectangles with equal sides and equal angles.- Diagonal is a line from one vertices to another that is non adjacent.
- 1 base / 12 edges / 5 faces / 8 vertexs / 2 base diagonals / 10 face diagonals / 4 space diagonals
Base Area of a Right Square Prism formula |
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| \( A_b \;=\; a^2 \) | ||
| Symbol | English | Metric |
| \( A_b \) = base area | \( in^2 \) | \( mm^2 \) |
| \( a \) = edge | \( in \) | \( mm \) |
Diagonal of a Right Square Prism formula |
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| \( D' \;=\; \sqrt { 2\cdot a^2 + h^2 } \) | ||
| Symbol | English | Metric |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
Edge of a Right Square Prism formulas |
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\( a \;=\; \dfrac{1}{2} \cdot \sqrt{2 \cdot D'^2 + 2 \cdot h^2} \) \( a \;=\; \dfrac{1}{2} \cdot \sqrt{4 \cdot h^2 + 2 \cdot A_s} \cdot -h \) \( a \;=\; \sqrt{ \dfrac{V} {h} } \) |
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| Symbol | English | Metric |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
Height of a Right Square Prism formulas |
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\( h \;=\; \dfrac{A_s}{4 \cdot a} - \dfrac{a}{2} \) \( h \;=\; \sqrt{D'^2 + 2 \cdot a^2} \) |
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| Symbol | English | Metric |
| \( h \) = height | \( in \) | \( mm \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( D' \) = space diagonal | \( in \) | \( mm \) |
| \( A_s \) = surface area | \( in^2 \) | \( mm^2 \) |
Surface Area of a Right Square Prism formula |
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| \( A_s \;=\; 2 \cdot a^2 + 4\;a \cdot h \) | ||
| Symbol | English | Metric |
| \( A_s \) = surface area (bottom, top, sides) | \( in^2 \) | \( mm^2 \) |
| \( a \) = area | \( in^2 \) | \( mm^2 \) |
| \( h \) = height | \( in \) | \( mm \) |
Volume of a Right Square Prism formula |
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| \( V \;=\; a^2 \cdot h \) | ||
| Symbol | English | Metric |
| \( V \) = volume | \( in^3 \) | \( mm^3 \) |
| \( a \) = edge | \( in \) | \( mm \) |
| \( h \) = height | \( in \) | \( mm \) |