Stretched Octagon Calculator

Name: Stretched Octagon - Geometry Calculator
Author: Jürgen Kummer

Calculations at a stretched or elongated octagon. This is a regular octagon where two parallel, opposite sides have been stretched, or alternatively have been shortened.
Enter two lengths and choose the number of decimal places. Then click Calculate.

Formulas:

l = a \cdot (1 + \sqrt{2}) + b - a

h = a \cdot (1 + \sqrt{2})

d = \sqrt{l^{2} + a^{2}}

p = 6 a + 2 b

A = 2 \cdot a^{2} \cdot (1 + \sqrt{2}) + h \cdot (b - a)

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

The octagon is a regular polygon with an even number of vertices. Therefore, elongating it does not alter its angles, unlike, for instance, the stretched pentagon, but similar to the stretched hexagon. The interior angles of the stretched octagon remain at 135 degrees.
The length of this shape is defined as the distance between the two opposite parallel sides farthest away from each other. The height is the distance between the two elongated sides. The diagonal is the distance from one vertex on one elongated side to the opposite vertex on the other elongated side. Two opposite sides are elongated by a length of b-a. Thus, the perimeter increases by 2*(b-a). The area is increased by the area of a rectangle with dimensions h*(b-a). If the elongation is negative, that is, if b is less than a, the result is a contraction. However, the calculation remains unchanged, as the value (b-a) simply becomes negative.

Of the eight axes of symmetry of a regular octagon, only two remain after stretching. The four axes of symmetry passing through the vertices vanish completely. Of those passing through opposite sides, two remain. The axis passing centrally through the elongated sides, and the axis passing centrally through the sides furthest apart, each perpendicular to the respective sides. Point symmetry about the center is preserved. Rotational symmetry now applies only to rotations of 180 degrees and multiples thereof.

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