Rectangular Hexagon Calculator

Name: Rectangular Hexagon - Geometry Calculator
Author: Jürgen Kummer

Calculations at a rectangular hexagon. A hexagon can only be rectangular if one vertex points inwards. Such a form can be made of a rectangle, where one vertex is rectangularly cut inside. The rectangular hexagon has five right interior angles and one of its counterpart, the 270-degrees angle, which is a right exterior angle.
Enter two lengths and two widths. Choose the number of decimal places, then click Calculate.

Formulas:

a = a^{'} + a^{″}

b = b^{'} + b^{″}

d = \sqrt{{a^{'}}^{2} + {b^{'}}^{2}}

p = 2 a + 2 b

A = a b - a^{″} b^{″}

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

The inward-facing vertex is concave, while the other five vertices are convex. This shape can also be viewed as a combination of two rectangles or two right trapezoids. Such a rectangular hexagon is formed when two rectangles are joined at a vertex and along sides of different lengths. In the case of two trapezoids, the slanted sides must be of equal length and the sum of the two acute angles must equal 90 degrees. These trapezoids are then joined along these slanted sides.

Such a rectangular hexagon typically lacks symmetry. Symmetry exists only in the special case where a′=b′ and a″=b″. In this instance, the diagonal serves as the axis of symmetry. Rectangular polygons with such onefold indents exist only with four, six, eight, or ten vertices. They are based on a rectangle with none to all corners folded inward, whereby each inward fold increases the total number of vertices by two. Two overlapping squares with two concave corners facing each other have two axes of symmetry.

Such shapes often arise during cutting, for instance when rectangular tiles do not fit exactly and must be adapted to inward-facing corners of a room. These inward-facing corners can also create such a shape as their base area, for example when a corner of a rectangular room is partitioned off from the rest to create an additional small room.

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