# Rhombus calculation

Description for the calculation of a rhombus

## Raute berechnen

A rhombus is a quadrangular geometric shape and has the following characteristics

• All four sides are the same length

• The angles of the opposite corners are identical

• The opposite sides are parallel to each other

## Legend

$$a$$   Length

$$h$$   Height

$$A$$   Area

$$P$$   Perimeter

$$e$$   Long diagonal

$$f$$   Short diagonal

$$α$$   Angle Alpha

$$β$$   Angle Beta ## Formulas for rhombus calculation

#### Calculate Area $$A$$ of a rhombus

$$A = a · h$$

$$\displaystyle A= \frac{e · f}{2}$$

$$A=a2 · sin(α)$$

#### Calculate Length $$a$$ of a rhombus

$$a = A / h$$

$$\displaystyle a = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2}$$

#### Calculate Height $$h$$ of a rhombus

$$\displaystyle h = \frac{A}{a}$$

$$h = sin(α) · a$$

$$b = sin(β) · a$$

#### Calculate Perimeter $$P$$ of a rhombus

$$P = 4 · a$$

$$\displaystyle P = 4 · \frac{h}{sin(α)}$$

$$\displaystyle P = 4 · \frac{h}{sin(β)}$$

#### Calculate long Diagonal $$e$$ of a rhombus

$$\displaystyle e =\frac{ h }{ sin(α/2)}$$

$$\displaystyle e = a ·\frac{ sin(β)}{ sin(α/2)}$$

$$\displaystyle e = 2 · a · cos\left(\frac{α}{2}\right)$$

#### Calculate short Diagonal $$f$$ of a rhombus

$$\displaystyle f =\frac{ h }{ sin(β/2)}$$

$$\displaystyle f = a ·\frac{ sin(α)}{ sin(β/2)}$$

$$\displaystyle f = 2 · a · cos\left(\frac{β}{2}\right)$$

#### Calculate Angle Beta $$β$$ of a rhombus

$$\displaystyle β =\frac{asin( h) }{a}$$