Square Heptagon Calculator

Name: Square Heptagon - Geometry Calculator
Author: Jürgen Kummer

Calculations at a square heptagon. Such a heptagon is formed by cutting off three corners or vertices of a square evenly and regularly. The cut off pieces are isosceles right triangles.
Enter the length of the original square and any other length, choose the number of decimal places and click Calculate.

Formulas:

b = a - \frac{d}{\sqrt{2}}

c = a - \sqrt{2} \cdot d

d = \sqrt{2} \cdot (a - b)

e = \sqrt{2} \cdot a - \frac{d}{2}

f = \sqrt{2} \cdot a - d

p = 2 b + 2 c + 3 d

A = a^{2} - \frac{3}{4} \cdot d^{2}

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

Removing all four vertices of a square in this manner creates a truncated square, a specific type of octagon. This is because slicing off the vertices replaces each removed vertex with two new ones. A corresponding pentagon or hexagon can of course be created in the same way by cutting off one or two vertices. This particular heptagon has been included here, unlike the corresponding pentagon and hexagon, because heptagons other than the regular heptagon are rarely encountered.

The square heptagon possesses one single axis of symmetry lying along the long diagonal. Otherwise, this shape has no symmetries. It features one right angle and six interior angles of 135 degrees. It has seven sides or edges, comprising three distinct types. Based on the terminology used here, there are two long sides, two short sides, and three slanted sides, with the slanted sides being shorter than the short sides. The long and short sides are remnants of the original square's sides, while the slanted sides are parallel and perpendicular to the diagonals. The diagonals of this square heptagon are those of the original square, shortened by half the length respectively the full length of a slanted side, corresponding to one or two heights of the removed isosceles right triangles. The perimeter and the area are smaller than those of the original square.

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