Rectangle

on . Posted in Plane Geometry

  • 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

Rectangle Index

 

Area of a Rectangle formula

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

 

Circumcircle Radius of a Rectangle formulas

\( R \;=\; D' \;/\;2    \) 

\( R \;=\; \sqrt{ a^2 + b^2 }  \;/\; 2 \)

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

\( C_x \;=\;   b \;/\; 2   \)

\( C_y \;=\; a \;/\; 2  \) 

Symbol English Metric
\( C \) = distance from centroid \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Elastic Section Modulus of a Rectangle formulas

\( S_x \;=\; a^2\; b \;/\; 6 \) 

\( S_y \;=\; a\;b^2 \;/\; 6 \) 

Symbol English Metric
\( S \) = elastic section modulus \( in^3 \) \( mm^3 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Perimeter of a Rectangle formulas

\(  P \;=\; 2\;a + 2\;b  \) 

\(  P \;=\; 2\; ( a + b)  \) 

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

 

Plastic Section Modulus of a Rectangle formulas

\(  Z_x \;=\; a^2 \;b \;/\; 4  \) 

\( Z_y \;=\;   a\;b^2 \;/\; 4  \)

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

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

\( J_{z1} \;=\; (a\;b\;/\;3) \; ( a^2 + b^2 )  \) 

Symbol English Metric
\( J \) = torsional constant \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Radius of Gyration of a Rectangle formulas

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

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

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

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

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

\( k_{z1} \;=\; \sqrt{  a^2 + b^2 \;/\; \sqrt{3} }  \)

Symbol English Metric
\( k \) = radius of gyration \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Second Moment of Area of a Rectangle formulas

\( I_{x} \;=\; a^3\; b\;/\;12 \) 

\( I_{y} \;=\; a\;b^3\;/\;12 \)

\( I_{x1} \;=\; a^3 \;b\;/\;3 \) 

\( I_{y1} \;=\; a\;b^3\;/\;3 \)

Symbol English Metric
\( I \) = moment of inertia \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

Side of a Rectangle formulas

\( a \;=\; (P\;/\;2) - b   \) 

\( b \;=\; (P\;/\;2) - a  \)

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

 

Torsional Constant of a Rectangle formula

\( J  \;=\; a^3\; b\; [\;  \frac{1}{3}  -  (0.21\;a\;/\;b)  \;  ( 1 - [ a^4 \;/\; 12\;b^4] \; ) \;]   \) 
Symbol English Metric
\( J \) = torsional constant \( in^4 \) \( mm^4 \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 

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Tags: Structural Steel Quadrilateral