# Tri-equilateral Trapezoid

on . 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
• 4 vertexs

## 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 $$\large{ in}$$ $$\large{ mm }$$