Area of a Self-intersecting Rectangle formula |
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| \( A_{area} \;=\; \dfrac{a \cdot b}{2} \) | ||
| Symbol | English | Metric |
| \( A_{area} \) = area | \( in^2\) | \( mm^2 \) |
| \( b, e \) = edge | \( in\) | \( mm \) |
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°.
Angle of a Self-intersecting Rectangle formulas
\( x \;=\; \dfrac{180° - z}{2} \)
\( z \;=\; arccos \left( \dfrac{2\cdot e^2 - b^2}{2\cdot e^2} \right) \)
\( w \;=\; 180° - z \)
Symbol English Metric \( x, y, z \) = angle \( deg\) \( rad\) \( w \) = intersection angle \( in\) \( mm \) \( b, e \) = edge \( in\) \( - x, y, z < 90°
- w > 90°
- b ∥ d
- a = c
- b = d
- e = f
- ∠A = ∠B = ∠C = ∠D
- ∠z + ∠w = 180°
- ∠x + ∠y + ∠z = 180°
- 4 edges
- 4 vertexs
Edge of a Self-intersecting Rectangle formula |
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| \) e \;=\; \dfrac{ \sqrt {a^2 + b^2} }{2} \( | ||
| Symbol | English | Metric |
| \) e \( = edge | \) in\( | \) mm \( |
| \) a, b \( = edge | \) in\( | \) mm \( |
Perimeter of a Self-intersecting Rectangle formula |
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| \) p \;=\; 2\cdot b + 4 \cdot e \( | ||
| Symbol | English | Metric |
| \) p \( = perimeter | \) in\( | \) mm \( |
| \) b, e \( = edge | \) in\( | \) mm $ |