# Rhomboid

Description for the calculation of rhomboids

## Calculate Rhomboids

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

• It has four sides and four corners

• The angles of the opposite corners are identical

• The opposite sides are parallel to each other and are the same length

• The diagonals have different lengths

## Legend

$$a$$   Length

$$b$$   Width

$$h_a$$   Height a

$$h_b$$   Height b

$$A$$   Area

$$P$$   Perimeter

$$e$$   Long diagonal

$$f$$   Short diagonal

$$α$$   Angle Alpha

$$β$$   Angle Beta

## Formulas for Rhomboid calculation

#### Calculate Area $$A$$ of a rhomboid

$$A = b · h_a$$

$$A=a · h_b$$

$$A=a · b· sin(α)$$

#### Calculate Length $$a$$ of a rhomboid

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

$$\displaystyle a = \frac{A}{b · sin(α)}$$

$$\displaystyle a = \frac{A }{ b · sin(β)}$$

#### Calculate Width $$b$$ of a rhomboid

$$\displaystyle b = \frac{A}{h_a}$$

$$\displaystyle b = \frac{A}{a · sin(α)}$$

$$\displaystyle b = \frac{A }{ a · sin(β)}$$

#### Calculate Height a $$h_a$$ of a rhomboid

$$\displaystyle h_a = \frac{A}{b}$$

$$\displaystyle h_a = sin(α) · a$$

$$\displaystyle h_a = sin(β) · a$$

#### Calculate Height b $$h_b$$ of a rhomboid

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

$$\displaystyle h_b= sin(α) ·b$$

$$\displaystyle h_b = sin(β) ·b$$

#### Calculate Perimeter $$P$$ of a rhomboid

$$\displaystyle P = 2 ·(a + b)$$

$$\displaystyle P = 2 · \frac{h_a}{sin(α)} + (2 · b)$$

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

$$\displaystyle e = \sqrt{a^2 + b^2 - 2 · a · b · cos(β)}$$

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

$$\displaystyle f = \sqrt{a^2 + b^2; - 2 · a · b · cos(α)}$$

#### Calculate Angle Alpha $$α$$ of a rhomboid

$$\displaystyle α = asin\left(\frac{A}{a · b}\right)$$