Tri-equilateral Trapezoid

on . Posted in Plane Geometry

  • tri equilateral trapezoid 3Tri-equilateral trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and having base angles that are the same with three congruent edges.
  • Acute angle measures less than 90°.
  • Congruent is all sides having the same lengths and angles measure the same.
  • Diagonal is a line from one vertices to another that is non adjacent.
  • Obtuse angle measures more than 90°.
  • a & c are bases
  • b & d are legs
  • a ∥ c
  • a ≠ c
  • a = b = d
  • ∠A & ∠D < 90°
  • ∠B & ∠C > 90°
  • ∠A = ∠D
  • ∠B = ∠C
  • ∠A + ∠B = 180°
  • ∠C + ∠D = 180°
  • 2 diagonals
  • 4 edges

Tri-equilateral Trapezoid Index

 

Acute Angle of a Tri-equilateral Trapezoid formulas

\(\large{  x = arccos \; \frac{g^2 \;+\; a^2 \;-\; h^2}{2\;g\;a} }\)     \(\large{ g = \frac{l\;c \;-\; a\;l}{2} }\) 

\(\large{  y =  180° - x  }\) 

Symbol English Metric
\(\large{ x }\) = acute angles \(\large{ deg}\) \(\large{ rad}\)
\(\large{ y }\) = obtuce angles \(\large{ deg}\) \(\large{ rad}\)
\(\large{ a, b, d }\) = equal length edges \(\large{ in}\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in}\) \(\large{ mm }\)

 

Area of a Tri-equilateral Trapezoid formula

\(\large{ A_{area} = \frac{c \;+\; b}{2} \; h   }\) 
Symbol English Metric
\(\large{ A_{area} }\) = area \(\large{ in^2}\) \(\large{ mm^2}\)
\(\large{ a, b, d }\) = equal length edges \(\large{ in}\) \(\large{ mm }\)
\(\large{ h }\) = height \(\large{ in}\) \(\large{ mm }\)
\(\large{ c }\) = unequal length edge \(\large{ in}\) \(\large{ mm }\)

  

Diagonal of a Tri-equilateral Trapezoid formula

\(\large{  d' = \sqrt{ a \; \left( c + a \right)  }  }\) 
Symbol English Metric
\(\large{ d', D' }\) = diagonal \(\large{ in}\) \(\large{ mm}\)
\(\large{ a, b, d }\) = equal length edges \(\large{ in}\) \(\large{ mm }\)
\(\large{ c }\) = unequal length edge \(\large{ in}\) \(\large{ mm }\)

 

Height of a Tri-equilateral Trapezoid formula

\(\large{ h = \frac{1}{2} \; \sqrt{ 4 \;a^2 - \left( c - a \right)^2 }   }\) 
Symbol English Metric
\(\large{ h }\) = height \(\large{ in}\) \(\large{ mm}\)
\(\large{ a, b, d }\) = equal length edges \(\large{ in}\) \(\large{ mm }\)
\(\large{ c }\) = unequal length edge \(\large{ in}\) \(\large{ mm }\)

 

Perimeter of a Tri-equilateral Trapezoid formula

\(\large{  P =  c + 3  a  }\) 
Symbol English Metric
\(\large{ P }\) = perimeter \(\large{ in}\) \(\large{ mm}\)
\(\large{ a, b, d }\) = equal length edges \(\large{ in}\) \(\large{ mm }\)
\(\large{ c }\) = unequal length edge \(\large{ in}\) \(\large{ mm }\)

 

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Tags: Quadrilateral