Rhombus Formulas

$$2p = S \times 4$$

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 Semi-Diagonal

$$\frac{d_{2}}{2} = \sqrt{ {S}^{2} - {\left(\frac{d_{1}}{2}\right)}^{2} }$$

Shorter Semi-Diagonal

Definition

A rhombus is a quadrilater with all sides congruent.

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 semi-diagonals
Diagonals makes four congruent right triangles, in which the hypotenuse is represented by the rhombus' side, and the cathetus' by the semi-diagonals