Self-intersecting Rectangle

Written by Jerry Ratzlaff 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

Area of a Self-intersecting Rectangle formula

\(\large{ A_{area} = \frac{a\;b}{2}  }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ b, e }\) = edge

Angle of a Self-intersecting Rectangle formula

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

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

\( \large{ w = 180° - z  }\)

Where:

\(\large{ x, y, z }\) = angle

\(\large{ w }\) = intersection angle

\(\large{ b, e }\) = edge

Edge of a Self-intersecting Rectangle formula

\(\large{ e = \frac{ \sqrt {a^2 + b^2} }{2}  }\)

Where:

\(\large{ e }\) = edge

\(\large{ a, b }\) = edge

Perimeter of a Self-intersecting Rectangle formula

\(\large{ p = 2\;b + 4\;e  }\)

Where:

\(\large{ p }\) = perimeter

\(\large{ b, e }\) = edge