# Rhombus

• Side of a rhombus: $$a$$
Diagonals of a rhombus: $${d_1}$$, $${d_2}$$
Consecutive angles: $$\alpha$$, $$\beta$$
Altitude: $$h$$
Radius of the inscribed circle: $$r$$
Perimeter: $$P$$
Area: $$S$$
1. A rhombus is a parallelogram in which all four sides are equal.
2. The sum of the angles adjacent to any side of a rhombus is $$180^\circ:$$
$$\alpha + \beta = 180^\circ$$
3. The diagonals of a rhombus are perpendicular and bisect each other.
4. If a rhombus has one right angle it is a square.
5. Relation between the sides and the diagonals of rhombus
$$d_1^2 + d_2^2 = 4{a^2}$$
6. Altitude of a rhombus
$$h = a\sin \alpha =$$ $${\large\frac{{{d_1}{d_2}}}{{2a}}\normalsize}$$
7. Radius of the inscribed circle
$$r = {\large\frac{h}{2}\normalsize} = {\large\frac{{a\sin \alpha }}{2}\normalsize} =$$ $${\large\frac{{{d_1}{d_2}}}{{4a}}\normalsize} =$$ $${\large\frac{{{d_1}{d_2}}}{{2\sqrt {d_1^2 + d_2^2} }}\normalsize}$$
8. Perimeter of a rhombus
$$P = 4a$$
9. Area of a rhombus
$$S = ah =$$ $${a^2}\sin \alpha =$$ $${\large\frac{{{d_1}{d_2}}}{2}\normalsize}$$