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Trapezoid

Area of a Trapezoid formulas

\(  A_{area} \;=\; h \cdot \left(  \dfrac{ c + a }{ 2 }  \right)   \) 

\(  A_{area} \;=\; m\cdot h   \) 
Symbol English Metric
\( A_{area} \) = area \( in^2 \) \( mm^2 \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)
\( m \) = midline \( in \) \( mm \)
  • trapezoid 12Trapezoid (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.

Diagonal of a Trapezoid formulas

\(  d' \;=\; \sqrt{  a^2 + b^2 - 2\cdot a\cdot \sqrt{ b^2 - h^2}  }  \) 

\(  D' \;=\; \sqrt{  a^2 + d^2 - 2\cdot a\cdot \sqrt{d^2 - h^2}  }  \) 
Symbol English Metric
\( d', D' \) = diagonal \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)
  • trapezoid 12a & c are bases
  • b & d are legs
  • a ∥ c
  • a ≠ c
  • ∠A + ∠B = 180°
  • ∠C + ∠D = 180°
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Distance from Centroid of a Trapezoid formulas

\(  C_x \;=\; \dfrac{ 2\cdot c\cdot g + c^2 + g\cdot a + c\cdot a + a^2 }{ 3 \left(  { c + a }  \right)  }   \)

\(  C_y \;=\; \dfrac{ h }{ 3} \cdot \left(  \dfrac{ 2c + a }{c + a}  \right)    \)
Symbol English Metric
\( C \) = distance from centroid \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)
\( g \) = offset \( in \) \( mm \)

 Piping Designer Logo 1trapezoid 12

 

 

 

 

 

 

 

Elastic Section Modulus of a Trapezoid formulas

\(  S_x \;=\; \dfrac{ I_x }{ C_y  }   \) 

\(  S_y \;=\; \dfrac{ I_y }{ C_x  }   \) 
Symbol English Metric
\( S \) = elastic section modulus \( in^3 \) \( mm^3 \)
\( C \) = distance from centroid \( in \) \( mm \)
\( I \) = moment of inertia \(lbm \;/\; ft^2-sec\)  \(kg \;/\;m^2\) 

trapezoid 12

 

 

 

 

 

 

 

Height of a Trapezoid formulas

\(  h \;=\; \dfrac{ 2\cdot A_{area} }{c + a}  \) 

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

 trapezoid 12

 

 

 

 

 

 

Midline of a Trapezoid formula
\(  m \;=\; \dfrac{a + c}{2}   \) 
Symbol English Metric
\( m \) = midline \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)

 trapezoid 12

 

 

 

 

 

Perimeter of a Trapezoid formulas

\(  P \;=\; a + b + c + d   \) 

\(  P \;=\; \sqrt {h^2 + g^2} + \sqrt {h^2 + \left( a - c - g  \right)^2   }  + a + c   \) 
Symbol English Metric
\( P \) = perimeter \( in \) \( mm \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)

 trapezoid 12

 

 

 

 

 

 

 

Plastic Section Modulus of a Trapezoid formulas

\(  Z_x \;=\; \dfrac{  h^2   \cdot  \left(  g\cdot c^2 + 14\cdot c\cdot a + g\cdot a^2   \right)  }{ 12\cdot \left(  c + a   \right)  }   \) 

\(  Z_y \;=\; \dfrac{  6\cdot c\cdot a\cdot h - 3\cdot c^2\cdot h - 8\cdot c + 8\cdot a + 4\;g^2 \cdot h - 8\cdot g  }{ 24}   \) 
Symbol English Metric
\( Z \) = plastic section modulus \( in^3 \) \( mm^3 \)
\( a, b, c, d \) = edge \( in \) \( mm \)
\( h \) = height \( in \) \( mm \)

trapezoid 12 

 

 

 

 

 

 

 

 

Edge of a Trapezoid formulas

\(  a \;=\;  2 \cdot \dfrac { A_{area} }{h} - c   \) 

\(  b \;=\; P - c - a - d   \) 

\(  c \;=\; 2 \cdot \dfrac {A_{area} }{h} - a   \) 

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

 trapezoid 12