Tri-equilateral Trapezoid

Written by Jerry Ratzlaff 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
  • 4 vertexs

Acute Angle of a Tri-equilateral Trapezoid formula

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

\(\large{  y =  180° - x  }\)

Where:

\(\large{ x }\) = acute angle

\(\large{ y }\) = obtuse angle

\(\large{ a, b, d }\) = equal length edges

\(\large{ h }\) = height

Area of an Tri-equilateral Trapezoid formula

\(\large{ A_{area} = \frac{c + b}{2} \; h   }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ a, b, d }\) = equal length edges

\(\large{ h }\) = height

\(\large{ c }\) = unequal length edge

Diagonal of a Tri-equilateral Trapezoid Formula

\(\large{  d' = \sqrt{ a \; \left( c + a \right)  }  }\)

Where:

\(\large{ d', D' }\) = diagonal

\(\large{ a, b, d }\) = equal length edges

\(\large{ c }\) = unequal length edge

Height of an Tri-equilateral Trapezoid formula

\(\large{ h = \frac{1}{2} \; \sqrt{ 4 \; a^2 - \left( c - a \right)^2 }   }\)

Where:

\(\large{ h }\) = height

\(\large{ a, b, d }\) = equal length edges

\(\large{ c }\) = unequal length edge

Perimeter of a Tri-equilateral Trapezoid formula

\(\large{  P =  c + 3 \; a  }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a, b, d }\) = equal length edges

\(\large{ c }\) = unequal length edge