

$$2p = S \times 4$$
Perimeter
$$S = \frac{2p}{4}$$
$$A = \frac{d_{1} \times d_{2}}{2}$$
Area
$$d_{1} = \frac{2A}{d_{2}}$$
Longer Diagonal
$$d_{2} = \frac{2A}{d_{1}}$$
Shorter Diagonal
$$S = \sqrt{ {\left(\frac{d_{1}}{2}\right)}^{2} + {\left(\frac{d_{2}}{2}\right)}^{2} }$$
Side (Pythagoras' theorem)
$$\frac{d_{1}}{2} = \sqrt{ {S}^{2}  {\left(\frac{d_{2}}{2}\right)}^{2} }$$
Longer SemiDiagonal
$$\frac{d_{2}}{2} = \sqrt{ {S}^{2}  {\left(\frac{d_{1}}{2}\right)}^{2} }$$
Shorter SemiDiagonal
Definition
A rhombus is a quadrilater with all sides congruent
Properties
 Four congruent sides, opposite sides are parallel
 Opposite angles are congruent, consecutive angles are supplementary (their sum is 180°)
 Diagonals are perpendicular
 Diagonals meet at a point called rhombus' center. The center divides the diagonals into two equal semidiagonals
 Diagonals makes four congruent right triangles, in which the hypotenuse is represented by the rhombus' side, and the cathetus' by the semidiagonals