Question 1113653: Parallelogram ABCD is a rhombus. Side BC = 5 cm and segment AO = 3.9 cm
Parallelogram image: https://imgur.com/Kq6O5Nb
I only need
the area of ABCD,
The length of Diagonal BD,
The measure of angle d1
and the tangent ratio of angle c2.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! By definition, all sides of a rhombus have the same length.
Also, the diagonals are perpendicular bisectors of each other.
Because of that, the diagonals divide the rhombus into 4 congruent right triangles.
For each of those triangles, the hypotenuse is a rhombus side, of length  ,
and one leg length is  .
Applying the Pythagorean theorem we can find the other length,  :
 .
Solving for  ,
 
Taking one leg as the base and the other leg as the height,
the area of each triangle can be calculated as
 ,
and the area of the rhombus (4 triangles) is
 
The length of diagonal BD is approximately
 ,
or we could say it is approximately  .
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