Trapezoid
Trapezoid (a two-dimensional figure) is a quadrilateral that has a pair of parallel opposite sides.- Acute angle measures less than 90°.
- Diagonal is a line from one vertices to another that is non adjacent.
- No interior angles are equal.
- Obtuse angle measures more than 90°.
- Quadrilateral (a two-dimensional figure) is a polygon with four sides.
- a & c are bases
- b & d are legs
- a ∥ c
- a ≠ c
- ∠A + ∠B = 180°
- ∠C + ∠D = 180°
- 2 diagonals
- 4 edges
- 4 vertexs
Article Links
Diagonal of a Trapezoid formulas |
||
|
\(\large{ d' = \sqrt{ a^2 \;+\; b^2 \;-\; 2\;a\; \sqrt{b^2 \;-\; h^2} } }\) \(\large{ D' = \sqrt{ a^2 \;+\; d^2 \;-\; 2\;a\; \sqrt{d^2 \;-\; h^2} } }\) |
||
| Symbol | English | Metric |
| \(\large{ d', D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Distance from Centroid of a Trapezoid formulas |
||
|
\(\large{ C_x = \frac{ 2\;c\;g \;+\; c^2 \;+\; g\;a \;+\; c\;a \;+\; a^2 }{ 3 \left( { c \;+\; a } \right) } }\) \(\large{ C_y = \frac { h }{ 3} \; \left( \frac{ 2c \;+\; a }{c \;+\; a} \right) }\) |
||
| Symbol | English | Metric |
| \(\large{ C }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ g }\) = offset | \(\large{ in }\) | \(\large{ mm }\) |
Elastic Section Modulus of a Trapezoid formulas |
||
|
\(\large{ S_x = \frac{ I_x }{ C_y } }\) \(\large{ S_y = \frac{ I_y }{ C_x } }\) |
||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \(\large{in^3}\) | \(\large{ mm^3 }\) |
| \(\large{ C }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec}}\) | \(\large{\frac{kg}{m^2}}\) |
Height of a Trapezoid formulas |
||
|
\(\large{ h = \frac { 2\; A_{area} }{c \;+\; a} }\) \(\large{ h = \frac { A_{area} }{m} }\) |
||
| Symbol | English | Metric |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Midline of a Trapezoid formula |
||
| \(\large{ m = \frac{a \;+\; c}{2} }\) | ||
| Symbol | English | Metric |
| \(\large{ m }\) = midline | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Perimeter of a Trapezoid formulas |
||
|
\(\large{ P = a + b + c + d }\) \(\large{ P = \sqrt {h^2 + g^2} + \sqrt {h^2 + \left( a - c - g \right)^2 } + a + c }\) |
||
| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Plastic Section Modulus of a Trapezoid formulas |
||
|
\(\large{ Z_x = \frac{ h^2 \; \left( g\;c^2 \;+\; 14\;c\;a \;+\; g\;a^2 \right) }{ 12\; \left( c \;+\; a \right) } }\) \(\large{ Z_y = \frac{ 6\;c\;a\;h \;-\; 3\;c^2\; h \;-\; 8\;c \;+\; 8\;a \;+\; 4\;g^2 \;h \;-\; 8\;g }{ 24} }\) |
||
| Symbol | English | Metric |
| \(\large{ Z }\) = plastic section modulus | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Trapezoid formulas |
||
|
\(\large{ J_{z} = I_x + I_y }\) \(\large{ J_{z1} = I_{x1} + I_{y1} }\) |
||
| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{mm^4 }\) |
| \(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec}}\) | \(\large{\frac{kg}{m^2}}\) |
Radius of Gyration of a Trapezoid formulas |
||
|
\(\large{ k_{x} = \frac {h}{6} \; \sqrt{ 2 + \frac{ 4\;c\;a}{ \left( c \;+\; a \right)^2 } } }\) \(\large{ k_{y} = \sqrt { \frac {I_y} {A_{area}} } }\) \(\large{ k_{z} = \sqrt { k_{x}{^2} + k_{y}{^2} } }\) \(\large{ k_{x1} = \frac{1}{6} \; \sqrt{ \frac{ 6\;h^2 \; \left( 3\;c \;+\; a \right) }{c \;+\; a} } }\) \(\large{ k_{y1} = \sqrt { \frac {I_{y1}} {A_{area}} } }\) \(\large{ k_{z1} = \sqrt { k_{x1}{^2} + k_{y1}{^2} } }\) |
||
| Symbol | English | Metric |
| \(\large{ k }\) = radius of gyration | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Second Moment of Area of a Trapezoid formulas |
||
|
\(\large{ I_{x} = \frac{ h^3 \; \left( c^2\; 4\;c\;a \;+\; a^2 \right) }{ 36 \; \left( c \;+\; a \right) } }\) \(\large{ I_{y} = \frac{ h \; \left( 4\;c\;a\;g^2 \;+\; 3\;c^2\; a\;g \;-\; 3\;c\;a^2\; g \;+\; c^4 \;+\; a^4 \;+\; 2\;c^3 \;a \;+\; c^2 \;g^2 \;+\; c^3 \;g \;+\; 2\;c\;a^3 \;-\; g\;a^3 \;+\; a^2\; g^2 \right) } { 36 \; \left( c \;+\; a \right) } }\) \(\large{ I_{x1} = \frac{ h^3 \; \left( 3\;c\;+\;a \right) }{12} }\) \(\large{ I_{y1} = \frac{ h \; \left( c^3 \;+\; 3\;c\;g^2 \;+\; 3\;c^2\; g \;+\; a^3 \;+\; g\;a^2 \;+\; c\;a^2 \;+\; a\;g^2 \;+\; 2\;c\;a\;g \;+\; a\;c^2 \right) }{12} }\) |
||
| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \(\large{in^4}\) | \(\large{mm^4}\) |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ k }\) = radius of gyration | \(\large{ in }\) | \(\large{ mm }\) |
Edge of a Trapezoid formulas |
||
|
\(\large{ a = 2 \; \frac { A_{area} }{h} - c }\) \(\large{ b = P - c - a - d }\) \(\large{ c = 2 \; \frac {A_{area} }{h} - a }\) \(\large{ d = P - c - a - b }\) |
||
| Symbol | English | Metric |
| \(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_{area} }\) = area | \(\large{ in }\) | |
| \(\large{ h }\) = height | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Inertia Structural Steel Modulus