Rectangle is a quadrilateral with two pair of parallel lines.- A rotated rectangle is a structural shape used in construction.
- Interior angles are 90°
- Exterior angles are 90°
- Angle \(\;A = B = C = D\)
- 2 diagonals
- 4 edges
- 4 vertexs
- See Article - Geometric Properties of Structural Shapes
Area of a Rotated Rectangle formula |
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\( A_{area} \;=\; a \cdot b \) (Area of a Rotated Rectangle) \( a \;=\; \dfrac{ A_{area} }{ b } \) \( b \;=\; \dfrac{ A_{area} }{ a } \) |
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| Symbol | English | Metric |
| \( A \) = area | \( in^2 \) | \( mm^2 \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Distance from Centroid of a Rotated Rectangle formulas |
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\( C_x \;=\; \dfrac { b \cdot cos( \theta) + a \cdot sin( \theta) } { 2 } \) \( C_y \;=\; \dfrac { a \cdot cos( \theta) + b \cdot sin( \theta) }{ 2 } \) |
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| Symbol | English | Metric |
| \( C \) = distance from centroid | \( in^2 \) | \( mm^2 \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Elastic Section Modulus of a Rotated Rectangle formula |
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| \( S_x \;=\; \dfrac{ b\cdot a\cdot \left(a^2 \cdot cos^2( \theta) + b^2 \cdot sin^2( \theta) \right) }{ 6 \cdot \left( a \cdot cos( \theta) + b\cdot sin( \theta) \right) } \) | ||
| Symbol | English | Metric |
| \( S \) = elastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Perimeter of a Rotated Rectangle formula |
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\( P \;=\; 2\cdot \left( a + b \right) \) (Perimeter of a Rotated Rectangle) \( a \;=\; \dfrac{ P - 2 \cdot b }{ 2 } \) \( b \;=\; \dfrac{ P - 2 \cdot a }{ 2 } \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Polar Moment of Inertia of a Rotated Rectangle formula |
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| \( J_{z} \;=\; \dfrac{b\cdot a}{3} \cdot \left( b^2 + a^2 \right) \) | ||
| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Radius of Gyration of a Rotated Rectangle formula |
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| \( k_{x} \;=\; \sqrt{ \dfrac{ a^2 \cdot cos^2 \left( b^2 \cdot sin^2( \theta) + \theta \right) }{ 2\cdot \sqrt{3} } } \) | ||
| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Second Moment of Area of a Rotated Rectangle formula |
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| \( k_{x} \;=\; \sqrt{ \dfrac{ a^2 \cdot cos^2 \left( b^2 \cdot sin^2( \theta) + \theta \right) }{ 2\cdot \sqrt{3} } } \) | ||
| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
Side of a Rotated Rectangle formulas |
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\( a \;=\; \dfrac{P}{2} - b \) \( b \;=\; \dfrac{P}{2} - a \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( a, b \) = edge | \( in \) | \( mm \) |
