# Formulas and Tables

Elementary Geometry# Rhombus

Diagonals of a rhombus: \({d_1}\), \({d_2}\)

Consecutive angles: \(\alpha\), \(\beta\)

Altitude: \(h\)

Radius of the inscribed circle: \(r\)

Perimeter: \(P\)

Area: \(S\)

- A rhombus is a parallelogram in which all four sides are equal.

- The sum of the angles adjacent to any side of a rhombus is \(180^\circ:\)

\(\alpha + \beta = 180^\circ\) - The diagonals of a rhombus are perpendicular and bisect each other.
- If a rhombus has one right angle it is a square.
- Relation between the sides and the diagonals of rhombus

\(d_1^2 + d_2^2 = 4{a^2}\) - Altitude of a rhombus

\(h = a\sin \alpha =\) \({\large\frac{{{d_1}{d_2}}}{{2a}}\normalsize}\) - Radius of the inscribed circle

\(r = {\large\frac{h}{2}\normalsize} = {\large\frac{{a\sin \alpha }}{2}\normalsize} =\) \({\large\frac{{{d_1}{d_2}}}{{4a}}\normalsize} =\) \({\large\frac{{{d_1}{d_2}}}{{2\sqrt {d_1^2 + d_2^2} }}\normalsize}\) - Perimeter of a rhombus

\(P = 4a\) - Area of a rhombus

\(S = ah =\) \({a^2}\sin \alpha =\) \({\large\frac{{{d_1}{d_2}}}{2}\normalsize}\)