A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent.
There are several formulas for the rhombus that have to do with its
 Sides(click for more detail)
 all 4 sides are congruent
 Angles(click for more detail)
 diagonals bisect vertex angles
 Diagonals(click for more detail)
 diagonals are pependicular
 Area (click for more detail)
A square is a rhombus and a rectangle. In other words, if each angle of a rhombus is 90°, then it's a square.
Probalby the most famous rhombus out there is the baseball diamond. The distance between each base is the same, making the shape a rhombus!
Rhombus Sides
All sides of a Rhombus are congruent.
AB BC CD ADRhombus Practice Problems
Since this shape is a rhombus you can set any of its sides equal to each other.

Related:
 Area of Rhombus
Diagonals of a Rhombus
 AOD = 90°
 AOB = 90°
 BOC = 90°
 COD = 90°
The shape below is not a rhombus because its diagonals are not perpendicular.
However, since opposite sides are congruent and parallel, and the diagonals bisect each other. The shape below is a paralelogram.

Related:
 Area of Rhombus
Anngles of a Rhombus
The diagonals bisect the vertex angles of a rhombus. A proof of this property of the diagonals
Problem 5
Problem 6
Since the diagonals of a rhombus are perpendicular, these outside angles must be complementary angles.
Problem 7
Since diagonals bisect vertex angles, BCA ACD
Problem 8

Related:
 Area of Rhombus
Area of Rhombus
Area = ½(diagonal_{1} × diagonal_{2})
Problem 9
Area = ½(IK ×HJ) = ½ (9 ×12) = 54
Putting It All Together
STAR is a rhombus. The measure of diagonalsSA is 24 and the measure of TR is 10, what is the perimeter of this rhombus?
Ask yourself: What is true about the angles formed by the diagonals of a rhombus?
The angles, are perpendicular!
Now, what is true about the diagonals of all parallelograms?
The diagonals of parallelograms bisect each other.
Therefore, ZA = 12, ZT = 5
What kind of triangle is ZTA?
A Right Triangle!
So you can use the pythagorean theorem to find the measure of side TA
Now, that you know the length of TA? How can you use the fact that the sides of a rhombus are congruent to finish this problem?
Since, all 4 sides must be 13.
The perimeter = 13 + 13 + 13 +13 = 52