Self-intersecting Rectangle

on . Posted in Plane Geometry

  • self intersecting rectangle 3Self-intersecting rectangle (a two-dimensional figure) is where one edge crosses over another.
  • Acute angle measures less than 90°.
  • Obtuse angle measures more than 90°.
  • x, y, z < 90°
  • w > 90°
  • b ∥ d
  • a = c
  • b = d
  • e = f
  • ∠A = ∠B = ∠C = ∠D
  • ∠z + ∠w = 180°
  • ∠x + ∠y + ∠z = 180°
  • 4 edges
  • 4 vertexs

Self-intersecting Rectangle Index

 

Area of a Self-intersecting Rectangle formula

\(\large{ A_{area} = \frac{a \;b}{2}  }\) 
Symbol English Metric
\(\large{ A_{area} }\) = area  \(\large{ in^2}\) \(\large{ mm^2}\)
\(\large{ b, e }\) = edge  \(\large{ in}\)  \(\large{ mm }\)

   

Angle of a Self-intersecting Rectangle formulas

\(\large{ x = \frac{180° \;-\; z}{2}  }\) 

\(\large{ z = arccos \left( \frac{2\;e^2 \;-\; b^2}{2\;e^2} \right) }\) 

\( \large{ w = 180° - z  }\) 

Symbol English Metric
\(\large{ x, y, z }\) = angle  \(\large{ deg}\) \(\large{ rad}\)
\(\large{ w }\) = intersection angle \(\large{ in}\)  \(\large{ mm }\)
\(\large{ b, e }\) = edge  \(\large{ in}\)  \(\large{ mm }\)

 

Edge of a Self-intersecting Rectangle formula

\(\large{ e = \frac{ \sqrt {a^2 \;+\; b^2} }{2}  }\) 
Symbol English Metric
\(\large{ e }\) = edge \(\large{ in}\)  \(\large{ mm }\)
\(\large{ a, b }\) = edge  \(\large{ in}\)  \(\large{ mm }\)

 

Perimeter of a Self-intersecting Rectangle formula

\(\large{ p = 2\; b + 4 \;e  }\) 
Symbol English Metric
\(\large{ p }\) = perimeter \(\large{ in}\)  \(\large{ mm }\)
\(\large{ b, e }\) = edge  \(\large{ in}\)  \(\large{ mm }\)

 

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Tags: Quadrilateral