Rhombus Formulas - XGeometry

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Rhombus

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

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