# Tri-equilateral Trapezoid

Written by Jerry Ratzlaff 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

## formulas that use Acute Angle of a Tri-equilateral Trapezoid

 $$\large{ x = arccos \; \frac{g^2 \;+\; a^2 \;-\; h^2}{2\;g\;a} }$$     $$\large{ g = \frac{l\;c \;-\; a\;l}{2} }$$ $$\large{ y = 180° - x }$$

### Where:

$$\large{ x }$$ = acute angle

$$\large{ y }$$ = obtuse angle

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

$$\large{ h }$$ = height

## formulas that use Area of an Tri-equilateral Trapezoid

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

### Where:

$$\large{ A_{area} }$$ = area

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

$$\large{ h }$$ = height

$$\large{ c }$$ = unequal length edge

## formulas that use Diagonal of a Tri-equilateral Trapezoid

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

### Where:

$$\large{ d', D' }$$ = diagonal

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

$$\large{ c }$$ = unequal length edge

## formulas that use Height of an Tri-equilateral Trapezoid

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

### Where:

$$\large{ h }$$ = height

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

$$\large{ c }$$ = unequal length edge

## formulas that use Perimeter of a Tri-equilateral Trapezoid

 $$\large{ P = c + 3 a }$$

### Where:

$$\large{ P }$$ = perimeter

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

$$\large{ c }$$ = unequal length edge