Square (a two-dimensional figure) is a quadrilateral with four equal side lengths and 90° interior angles.- Abbreviated as SQ
- Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
- Diagonal is a line from one vertices to another that is non adjacent.
- Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
- Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
- Quadrilateral (a two-dimensional figure) is a polygon with four sides.
- a ∥ c
- b ∥ d
- a = b = c = d
- ∠A = ∠B = ∠C = ∠D = 360°
- 4 interior angles are 90°
- 2 diagonals
- 4 edges
- 4 vertex
- See Article - Geometric Properties of Structural Shapes
Area of a Square formulas |
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\( A_{area} \;=\; a^2 \) \( A_{area} \;=\; \dfrac{ D'^2 }{ 2 }\) \( A_{area} \;=\; 4 \cdot r^2 \) \( A_{area} \;=\; 2 \cdot R^2 \) |
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| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
Circumcircle Radius of a Square formulas |
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\( R \;=\; \dfrac{ a }{ \sqrt {2} }\) \( R \;=\; \dfrac{ D' }{ 2 }\) |
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| Symbol | English | Metric |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Diagonal of a Square formulas |
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\( D' \;=\; a \cdot \sqrt {2} \) \( D' \;=\; \sqrt {2 \cdot A_{area} } \) \( D' \;=\; 2 \cdot R \) \( D' \;=\; 2 \cdot r \cdot \sqrt{2} \) \( D' \;=\; 2 \cdot R \) \( D' \;=\; \dfrac{ P }{ 2 \cdot \sqrt{2} }\) |
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| Symbol | English | Metric |
| \( D' \) = diagonal | \( in \) | \(\large{ mm }\) |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( P \) = perimeter | \( in \) | \( mm \) |
Distance from Centroid of a Square formulas |
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\( C_x \;=\; \dfrac{ a }{ 2 }\) \( C_y \;=\; \dfrac{ a }{ 2 }\) |
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| Symbol | English | Metric |
| \( C \) = distance from centroid | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Elastic Section Modulus of a Square formulas |
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| \( S \;=\; \dfrac{ a^3 }{ 6 }\) | ||
| Symbol | English | Metric |
| \( S \) = elastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Inscribed Circle Radius of a Square formulas |
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\( r \;=\; \dfrac{ a}{ 2 } \) \( r \;=\; \dfrac{ P}{ 8 } \) \( r \;=\; \dfrac{ D }{ 2\cdot \sqrt{2} } \) \( r \;=\; \dfrac{ \sqrt{A_{area} } }{ 2 } \) \( r \;=\; \dfrac{ R}{ \sqrt{2} }\) |
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| Symbol | English | Metric |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
| \( P \) = perimeter | \( in \) | \( mm \) |
Perimeter of a Square formulas |
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\( P \;=\; 4 \cdot a \) \( P \;=\; 4\cdot \sqrt{A_{area} } \) \( P \;=\; 2\cdot D'\cdot \sqrt{2} \) \( P \;=\; 4\cdot R\cdot \sqrt{2} \) \( P \;=\; 8\cdot r \) |
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| Symbol | English | Metric |
| \( P \) = perimeter | \( in \) | \( mm \) |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
| \( D' \) = diagonal | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( r \) = inside radius | \( in \) | \( mm \) |
| \( R \) = outside radius | \( in \) | \( mm \) |
Side of a Square formulas |
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| \( a \;=\; \sqrt{ A_{area} } \) | ||
| Symbol | English | Metric |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
| \( A_{area} \) = area | \( in^2 \) | \( mm^2 \) |
Plastic Section Modulus of a Square formulas |
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| \( Z \;=\; \dfrac{ a^3 }{ 4 } \) | ||
| Symbol | English | Metric |
| \( Z \) = plastic section modulus | \( in^3 \) | \( mm^3 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Polar Moment of Inertia of a Square formulas |
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\( J_{z} \;=\; \dfrac{ a^4}{ 6 }\) \( J_{z1} \;=\; \dfrac{ 2\cdot a^4}{ 3 }\) |
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| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Radius of Gyration of a Square formulas |
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\( k_{x} \;=\; \dfrac{ a }{ 2\cdot \sqrt{3} }\) \( k_{y} \;=\; \dfrac{ a }{ 2\cdot \sqrt{3} }\) \( k_{z} \;=\; \dfrac{ a }{ \sqrt{6} }\) \( k_{x1} \;=\; \dfrac{ a }{ \sqrt{3} }\) \( k_{y1} \;=\; \dfrac{ a }{ \sqrt{3} }\) \( k_{z1} \;=\; \sqrt{ \frac {2}{3} \cdot a } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Second Moment of Area of a Square formulas |
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\( I_{x} \;=\; \dfrac{ a^4}{ 12 }\) \( I_{y} \;=\; \dfrac{ a^4}{ 12 }\) \( I_{x1} \;=\; \dfrac{ a^4}{ 3 }\) \( I_{y1} \;=\; \dfrac{ a^4}{ 3 }\) |
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| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
Torsional Constant formulas |
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| \( J \;=\; 2.25 \cdot \left( \dfrac{ a }{ 2 } \right)^4 \) | ||
| Symbol | English | Metric |
| \( J \) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \( a, b, c, d \) = edge | \( in \) | \( mm \) |
