Tri-equilateral Trapezoid Calculator

Name: Tri-equilateral Trapezoid - Geometry Calculator
Author: Jürgen Kummer

Calculations at a trapezoid with three equal sides, a special case of an isosceles trapezoid. Both legs and one of the two parallel sides have the same length.
Enter both side lengths, choose the number of decimal places and click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:

d = \sqrt{b \cdot (a + b)}

h = \frac{1}{2} \cdot \sqrt{4 b^{2} - {(a - b)}^{2}}

r_{c} = b \cdot \sqrt{\frac{b \cdot (a + b)}{4 b^{2} - {(a - b)}^{2}}}

p = a + 3 \cdot b

A = \frac{a + b}{2} \cdot h

g = \frac{| a - b |}{2}

α = \arccos (\frac{g^{2} + b^{2} - h^{2}}{2 \cdot g \cdot b})

β = 180 ° - α

Side lengths, diagonal, height, radius and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

There are two different types of tri-equilateral trapezoids, which can be called acute and obtuse tri-equilateral trapezoids, depending on whether the unequal side is shorter or longer than the other three sides. Both of these types are axially symmetrical through the perpendicular bisector of the two parallel sides, but have no other symmetries. The calculation is the same in both cases.
Tri-equilateral trapezoids are difficult to recognize because the slanted sides make the equal-length base appear shorter. This applies to both types of this special shape. This is an optical illusion that is difficult to fully explain, but it may be related to the well-known Müller-Lyer illusion. Part of the effect is due to the fact that slanted lines create an impression of depth and therefore appear longer than horizontal or vertical ones. However, the illusion remains even when the trapezoid is rotated.
An equilateral trapezoid, i.e. one in which all sides are the same length, is a rhombus or a square.

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