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Rectangle

  • rectangle 8Rectangle (a two-dimensional figure) is a quadrilateral with two pair of parallel edges.
  • 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.
  • 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 = c
  • b = d
  • ∠A = ∠B = ∠C = ∠D = 360°
  • 4 interior angles are 90°
  • 2 diagonals
  • 4 edges
  • 4 vertexs

 

Area of a Rectangle formula
\( A_{area} \;=\; a \cdot b  \) 
Symbol English Metric
\( A_{area} \) = area  \( in^2 \) \( mm^2 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Circumcircle Radius of a Rectangle formulas

\( R \;=\;  \dfrac{ D' }{2  }  \) 

\( R \;=\;  \dfrac{\sqrt{ a^2 + b^2 }  }{ 2 }\)
Symbol English Metric
\( R \) = outside radius \( in \) \( mm \)
\( D' \) = diagonal \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Diagonal of a Rectangle formula
\( D' \;=\; \sqrt {a^2 + b^2 } \) 
Symbol English Metric
\( D' \) = diagonal \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Distance from Centroid of a Rectangle formulas

\( C_x \;=\;  \dfrac{ b }{ 2 }  \)

\( C_y \;=\; \dfrac{ a }{ 2 } \) 
Symbol English Metric
\( C \) = distance from centroid \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Elastic Section Modulus of a Rectangle formulas

\( S_x \;=\; \dfrac{ a^2\cdot b }{ 6 }\) 

\( S_y \;=\; \dfrac{ a \cdot b^2 }{ 6 }\) 
Symbol English Metric
\( S \) = elastic section modulus \( in^3 \) \( mm^3 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Perimeter of a Rectangle formulas

\(  P \;=\;  2 \cdot a + 2 \cdot b  \) 

\(  P \;=\; 2 \cdot ( a + b)  \) 
Symbol English Metric
\( P \) = perimeter \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Plastic Section Modulus of a Rectangle formulas

\(  Z_x \;=\; \dfrac{ a^2 \cdot b }{ 4 } \) 

\( Z_y \;=\;   \dfrac{ a \cdot b^2 }{ 4 } \)
Symbol English Metric
\( Z \) = plastic section modulus \( in^3 \) \( mm^3 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Polar Moment of Inertia of a Rectangle formulas

\( J_{z} \;=\;  \dfrac{ a \cdot b }{ 12 } \cdot ( a^2 + b^2 )  \) 

\( J_{z1} \;=\;  \dfrac{ a \cdot b }{ 3 } \cdot ( a^2 + b^2 )  \) 
Symbol English Metric
\( J \) = torsional constant \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Radius of Gyration of a Rectangle formulas

\( k_{x} \;=\;   \dfrac{ a }{ 2 \cdot \sqrt{3} } \) 

\( k_{y} \;=\;   \dfrac{  b }{ 2 \cdot \sqrt{3} } \) 

\( k_{z} \;=\;   \sqrt{  \dfrac{ a^2 + b^2 }{ 2 \cdot \sqrt{3} } } \) 

\( k_{x1} \;=\;  \dfrac{  a }{  \sqrt{3}  }\)

\( k_{y1} \;=\;  \dfrac{  b }{  \sqrt{3} } \)

\( k_{z1} \;=\; \sqrt{  \dfrac{ a^2 + b^2 }{ \sqrt{3} } } \)
Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Second Moment of Area of a Rectangle formulas

\( I_{x} \;=\;  \dfrac{ a^3\cdot b}{12 }\) 

\( I_{y} \;=\;  \dfrac{ a\cdot b^3}{12 }\)

\( I_{x1} \;=\;  \dfrac{ a^3 \cdot b}{3 }\) 

\( I_{y1} \;=\;  \dfrac{ a\cdot b^3}{3 }\)
Symbol English Metric
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Side of a Rectangle formulas

\( a \;=\;   \dfrac{ P}{2 } - b   \) 

\( b \;=\;  \dfrac{P}{2} - a  \)
Symbol English Metric
\( a, b, c, d \) = edge \( in \) \( mm \)
\( P \) = perimeter \( in \) \( mm \)

 

Torsional Constant of a Rectangle formula
\( J  \;=\;  a^3 \cdot b \cdot    \left(     \dfrac{1}{3}   -  \dfrac{ 0.21 \cdot a }{ b }   \cdot   \left(  1 -   \left( \dfrac{ a^4 }{ 12 \cdot b^4 } \right)   \right)   \right)   \) 
Symbol English Metric
\( J \) = torsional constant \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

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