Tri-equilateral Trapezoid

on 03 May 2019. Posted in Plane Geometry

Tri-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

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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Acute Angle of a Tri-equilateral Trapezoid formulas