Calculations at an isosceles trapezoid (or isosceles trapezium). This is a trapezoid with two opposite legs of equal length with mirrored angles.
Enter the three 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 = √ a * b + c²
h = 1/2 * √ 4c² - ( a - b )²
m = ( a + b ) / 2
rc = c * √ ( a * b + c² ) / ( 4c² - ( a - b )² )
g = ( a - b ) / 2
p = a + b + 2 * c
A = 1/4 * √ ( a + b )² * ( a - b + 2c ) * ( b - a + 2c ) = m * h
α = arccos( ( g² + c² - h² ) / ( 2 * g * c ) )
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).
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The perpendicular bisectors intersect at the circumcircle center. The perpendicular bisector of the two parallel sides is the symmetry axis of the isosceles trapezoid.The isosceles trapezoid is therefore axially symmetric, but neither point-symmetric nor rotationally symmetric.
perpendicular bisectors and circumcircle
An isosceles trapezoid is created when you cut off the tip of an isosceles triangle. Isosceles trapezoids can be used to tile a plane without gaps by placing the trapezoids next to each other on their slanted sides in each row, each rotated by 180 degrees. If you depict a square or a rectangle in the middle of the vanishing point perspective, it appears in the shape of an isosceles trapezoid.
The two diagonals of the isosceles trapezoid have the same length. This is in contrast to the parallelogram, which is created when both sides have equal angles rather than mirrored ones. The parallelogram can be viewed as an isosceles obtuse trapezoid.
A special case of the isosceles trapezoid is the tri-equilateral trapezoid, in which the long or short of the two parallel sides has the length of the legs. There are therefore two different variants of this. An isosceles and simultaneously right trapezoid would of course be a rectangle.
