Parallelogram
Parallelogram is a quadrilateral with two pair of parallel edges.- Opposite sides are congurent and parallel.
- Opposite angles equal, having more or less 90°.
- 2 diagonals
- 4 edges
- 4 vertexs
Angle of a Parallelogram formula
\(\large{ cos \; x = \frac {a^2 \;+\; b^2 \;-\; d'^2 }{2ab} }\)
\(\large{ cos \; y = \frac {a^2 \;+\; b^2 \;-\; D'^2 }{2ab} }\)
\(\large{ sin \; x = sin \; y \; \frac {A }{ab} }\)
Area of a Parallelogram formula
\(\large{ A = bh }\)
Diagonal of a Parallelogram formula
\(\large{ d' = \sqrt{ a^2 \;+\; b^2 \;-\; 2ab \; cos \; x } }\)
\(\large{ d' = \sqrt{ a^2 \;+\; b^2 \;+\; 2ab \; cos \; y } }\)
\(\large{ D' = \sqrt{ a^2 \;+\; b^2 \;-\; 2ab \; cos \; y } }\)
\(\large{ D' = \sqrt{ a^2 \;+\; b^2 \;+\; 2ab \; cos \; x } }\)
\(\large{ d' = \sqrt{ 2a^2 \;+\; 2b^2 \;-\; D'^2 } }\)
\(\large{ D' = \sqrt{ 2a^2 \;+\; 2b^2 \;-\; d'^2 } }\)
Edge of a Parallelogram formula
\(\large{ a = \frac {P}{2} - b }\)
\(\large{ b = \frac {P}{2} - a }\)
\(\large{ b = \frac {A}{h} }\)
\(\large{ a = \frac {h_b}{sin\; x} }\)
\(\large{ a = \frac {h_b}{sin\; y} }\)
\(\large{ b = \frac {h_a}{sin\; x} }\)
\(\large{ b = \frac {h_a}{sin\; y} }\)
\(\large{ a = \sqrt{ \frac {D'^2 \;+\; d'^2 \;-\; 2b^2 }{2} } }\)
\(\large{ b = \sqrt{ \frac {D'^2 \;+\; d'^2 \;-\; 2a^2 }{2} } }\)
Height of a Parallelogram formula
\(\large{ h_a = \frac {A}{b} }\)
\(\large{ h_a = b \; sin \; x }\)
\(\large{ h_a = b \; sin \; y }\)
\(\large{ h_b = a \; sin \; x }\)
\(\large{ h_b = a \; sin \; y }\)
Perimeter of a Parallelogram formula
\(\large{ P = 2 \left( a+b \right) }\)
Where:
\(\large{ A }\) = area
\(\large{ a, b }\) = edge
\(\large{ A, B, C, D }\) = vertex
\(\large{ d', D' }\) = diagonal
\(\large{ h_a, h_b }\) = height
\(\large{ P }\) = perimeter
\(\large{ x }\) = acute angles
\(\large{ y }\) = obtuce angles