# Self-intersecting Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Self-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 formulas

 $$\large{ x = \frac{180° \;-\; z}{2} }$$ $$\large{ z = arccos \left( \frac{2\;e^2 \;-\; b^2}{2\;e^2} \right) }$$ $$\large{ w = 180° - z }$$

### 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