SOLUTION: 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

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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