Rhombus

Written by Jerry Ratzlaff on . Posted in Plane Geometry

rhombus 2Arhombus 1B

Rhombus

  • Rhombus is a quadrilateral with two pair of parallel edges.
  • All edges are equal in length and opposite angles are equal.
  • 4 angle
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Area of a Rhombus formula

\(\large{ A = \frac {D' \; d' } {2} }\)

Angle of a Rhombus formula

\(\large{ sin \; x =  \frac {2D'd'}{D'^2 \;+\; d'^2}  }\)

\(\large{ sin \; y =  \frac {2D'd'}{D'^2 \;+\; d'^2}  }\)

\(\large{ cos \; x = 1 \;-\; \frac {d'^2}{2a^2}  }\)

\(\large{ cos \; x = \frac {D'^2}{2a^2} \;-\; 1 }\)

\(\large{ cos \; y = 1 \;-\; \frac {D'^2}{2a^2}  }\)

\(\large{ cos \; y = \frac {d'^2}{2a^2} \;-\; 1 }\)

\(\large{ sin \; x =  \frac {A}{a^2 }  }\)

\(\large{ sin \; y =  \frac {A}{a^2 }  }\)

Diagonal of a Rhombus formula

\(\large{ d' = \frac {2A}{D'} }\)

\(\large{ D' = \frac {2A}{d'} }\)

\(\large{ d' =  \sqrt{  4\; a^2 \;-\; D'^2  }   }\)

\(\large{ D' =  \sqrt{  4\; a^2 \;-\; d'^2  }   }\)

\(\large{ d' = a  \sqrt{  2\;-\; 2 \; cos \; x }   }\)

\(\large{ d' = a  \sqrt{  2\;+\; 2 \; cos \; y }   }\)

\(\large{ D' = a  \sqrt{  2\;-\; 2 \; cos \; y }   }\)

\(\large{ D' = a  \sqrt{  2\;+\; 2 \; cos \; x }   }\)

\(\large{ d' = 2a \; cos \left(  \frac{y}{ 2} \right)    }\)

\(\large{ d' = 2a \; sin \left(  \frac{x}{ 2} \right)    }\)

\(\large{ D' = 2a \; cos \left(  \frac{x}{ 2} \right)    }\)

\(\large{ D' = 2a \; sin \left(  \frac{y}{ 2} \right)    }\)

Edge of a Rhombus formulacos

\(\large{ a = \frac {P} {4} }\)

\(\large{ a = \frac { \sqrt { {D'}^2 \;+\; {D'}^2 } } { 2 }   }\)

\(\large{ a =   \sqrt{  \frac{ A }{ sin\;x }  }   }\)

\(\large{ a =   \sqrt{  \frac{ A }{ sin\;y }  }   }\)

\(\large{ a = \frac {d'} { \sqrt{ 2 \;-\; 2 \; cos\; x }    }  }\)

\(\large{ a = \frac {d'} { \sqrt{ 2 \;+\; 2 \; cos\; y }    }  }\)

\(\large{ a = \frac {D'} { \sqrt{ 2 \;-\; 2 \; cos\; y }    }  }\)

\(\large{ a = \frac {D'} { \sqrt{ 2 \;+\; 2 \; cos\; x }    }  }\)

\(\large{ a =   \sqrt{  \frac{ D' \; d' }{ 2 \; sin \; x }  }   }\)

 \(\large{ a =   \sqrt{  \frac{ D' \; d' }{ 2 \; sin \; y }  }   }\)

Perimeter of a Rhombus formula

\(\large{ P = 4a }\)

 

Where:

\(\large{ A }\) = area

\(\large{ a }\) = edge

\(\large{ A,\; B,\; C,\; D }\) = vertex

\(\large{ d',\; D' }\) = diagonal

\(\large{ P }\) = perimeter

\(\large{ x }\) = acute angle

\(\large{ y }\) = obtuse angle