Tri-equilateral Trapezoid

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
\( x \;=\; arccos \left( \dfrac{ g^2 + a^2 - h^2 }{ 2\cdot g\cdot a} \right)\) \( g \;=\; \dfrac{l\cdot c - a\cdot l}{2} \) \( y \;=\; 180° - x \)
Symbol	English	Metric
\( x \) = acute angles	\( deg\)	\( rad\)
\( y \) = obtuce angles	\( deg\)	\( rad\)
\( a, b, d \) = equal length edges	\( in\)	\( mm \)
\( h \) = height	\( in\)	\( mm \)

Area of a Tri-equilateral Trapezoid formula
\( A_{area} \;=\; \dfrac{c + b}{2} \cdot h \)
Symbol	English	Metric
\( A_{area} \) = area	\( in^2\)	\( mm^2\)
\( a, b, d \) = equal length edges	\( in\)	\( mm \)
\( h \) = height	\( in\)	\( mm \)
\( c \) = unequal length edge	\( in\)	\( mm \)

Diagonal of a Tri-equilateral Trapezoid formula
\( d' \;=\; \sqrt{ a \cdot \left( c + a \right) } \)
Symbol	English	Metric
\( d', D' \) = diagonal	\( in\)	\( mm \)
\( a, b, d \) = equal length edges	\( in\)	\( mm \)
\( c \) = unequal length edge	\( in\)	\( mm \)

Height of a Tri-equilateral Trapezoid formula
\( h \;=\; \dfrac{1}{2} \cdot \sqrt{ 4 \cdot a^2 - \left( c - a \right)^2 } \)
Symbol	English	Metric
\( h \) = height	\( in\)	\( mm \)
\( a, b, d \) = equal length edges	\( in\)	\( mm \)
\( c \) = unequal length edge	\( in\)	\( mm \)

Perimeter of a Tri-equilateral Trapezoid formula
\( P \;=\; c + 3 \cdot a \)
Symbol	English	Metric
\( P \) = perimeter	\( in\)	\( mm \)
\( a, b, d \) = equal length edges	\( in\)	\( mm \)
\( c \) = unequal length edge	\( in\)	\( mm \)