How do you find the diagonal of a parallelogram

1.  Diagonals of a parallelogram if you know sides and angle or sides and other diagonal

 

diagonal parallelogram1

     d blue1    - smaller  diagonal

     DD blue    - larger  diagonal

    a black , b black      -  sides

     alpha red  -  acute angle

     beta green  -  obtuse angle

 

Find length of diagonals of a parallelogram if given sides and angle ( D d /) :

diagonal parallelogram1 F1 a

diagonal parallelogram1 F2 a

 

diagonal parallelogram1 F3 a

diagonal parallelogram1 F4 a

 

Find length of diagonal of a parallelogram if given sides and other diagonal ( D d ) :

diagonal parallelogram1 F d

diagonal parallelogram1 F1 d

 

 

2.  Diagonals of a parallelogram if you know area, angle between the diagonals and other diagonal

 

diagonal parallelogram2

     d blue1    - smaller  diagonal

     DD blue    - larger  diagonal

    alpha red , beta green     -  angles between the diagonals

   A18 black  - area  of a parallelogram

 

Find length of diagonal of a parallelogram if given area, angle between the diagonals and other diagonal ( D d ) :

diagonal parallelogram2 A F1

diagonal parallelogram2 A F2