Parallelogram

Written by Jerry Ratzlaff on . Posted in Plane Geometry

parallelogram 2Aparallelogram 1A

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