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


\(a\)   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

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