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Rectangle

See Article - Geometric Properties of Structural Shapes

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	$in$	$mm$

Rectangle (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.

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	$in$	$mm$

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

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

∠A = ∠B = ∠C = ∠D = 360°
4 interior angles are 90°
2 diagonals
4 edges
4 vertexs

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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