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xGeometry

Rhombus

Longer Diagonal
$$d_{1}$$
Shorter Diagonal
$$d_{2}$$
Side
$$S$$
Longer Semi-Diagonal
$$\frac{d_{1}}{2}$$
Shorter Semi-Diagonal
$$\frac{d_{2}}{2}$$
$$2p = S \times 4$$
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
Properties
  1. Four congruent sides, opposite sides are parallel
  2. Opposite angles are congruent, consecutive angles are supplementary (their sum is 180°)
  3. Diagonals are perpendicular
  4. Diagonals meet at a point called rhombus' center. The center divides the diagonals into two equal semi-diagonals
  5. Diagonals makes four congruent right triangles, in which the hypotenuse is represented by the rhombus' side, and the cathetus' by the semi-diagonals