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 |
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\( x \;=\; arccos \left( \dfrac{ g^2 + a^2 - h^2 }{ 2\cdot g\cdot a} \right)\) \( g \;=\; \dfrac{l\cdot c - a\cdot l}{2} \) \( y \;=\; 180° - x \) |
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| 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 |
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| \( A_{area} \;=\; \dfrac{c + b}{2} \cdot h \) | ||
| 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 |
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| \( d' \;=\; \sqrt{ a \cdot \left( c + a \right) } \) | ||
| 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 |
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| \( h \;=\; \dfrac{1}{2} \cdot \sqrt{ 4 \cdot a^2 - \left( c - a \right)^2 } \) | ||
| 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 |
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| \( P \;=\; c + 3 \cdot a \) | ||
| Symbol | English | Metric |
| \( P \) = perimeter | \( in\) | \( mm \) |
| \( a, b, d \) = equal length edges | \( in\) | \( mm \) |
| \( c \) = unequal length edge | \( in\) | \( mm \) |
