Right Trapezoid

on . Posted in Plane Geometry

  • right trapezoid 7Right trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and two adjacent right angles.
  • Acute angle is an angle that measures less than 90°.
  • Obtuse angle is an angle that measures more than 90°.
  • a & c are bases
  • b & d are legs
  • a ∥ c
  • a ≠ c
  • b ≠ d
  • ∠A < 90°
  • ∠B > 90°
  • ∠C = ∠D
  • ∠A + ∠B = 180°
  • ∠C + ∠D = 180°

Right Trapezoid Index

 

Angle of a Right Trapezoid formulas

\(\large{  x = 90° - arccos \;  \frac{ d^2 \;+\; b^2 \;-\; \left(a \;-\; c \right)^2 }{ 2\;d\;b }  }\) 

\(\large{  y =  180° - x }\) 

Symbol English Metric
\(\large{ x }\) = acute angles \(\large{ deg}\) \(\large{ rad}\)
\(\large{ y }\) = obtuce angles \(\large{ deg}\) \(\large{ rad}\)
\(\large{ a, b, c, d }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Area of a Right Trapezoid formula

\(\large{  A_{area} = \frac{1}{2} \; d \; \left( a + c \right)   }\) 
Symbol English Metric
\(\large{ A_{area} }\) = area \(\large{ in^2}\) \(\large{ mm^2}\)
\(\large{ a, b, c, d }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

Diagonal of a Right Trapezoid formulas

\(\large{  d' =  \sqrt{c^2+d^2}   }\) 

\(\large{  D' = \sqrt{a^2+d^2}   }\) 

Symbol English Metric
\(\large{ d', D' }\) = diagonal \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, b, c, d }\) = edge \(\large{ in}\) \(\large{ mm }\)

  

Midline of a Right 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 RIGHT Trapezoid formula

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

 

Side of a Right Trapezoid formulas

\(\large{  b = \sqrt{ \left( a-c \right)^2 + d^2  }  }\) 

\(\large{  d = \sqrt{ b^2 - \left( a - c \right)^2  }  }\) 

Symbol English Metric
\(\large{ b, d }\) = edge \(\large{ in}\) \(\large{ mm }\)
\(\large{ a, c }\) = edge \(\large{ in}\) \(\large{ mm }\)

 

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Tags: Quadrilateral