Rhombus

Rhombus formulas

Notations

a : Side
A : Acute angle (smallest angle between A and B. A <= 90 degree)
B : Obtuse angle (highest angle between A and B. B >= 90 degree)
C : Opposite angle to A
D : Opposite angle to B
d₁ : smallest diagonal
d₂ : highest diagonal
h : Height
A_r : Area
P : Perimeter

Side

Relationship between the side and diagonals

`a=sqrt(d_1^2+d_2^2)/2`

Angles

In a Rhombus, opposite angles are equivalent and adjacent angles are supplementary.

`A=C=180°-B=180°-D`

`B=D=180°-A=180°-C`

`A+B+C+D=360°`

Diagonals

`d_1=2*a*sin(A/2)`

`d_2=2*a*cos(A/2)`

Relationship between angles and diagonals :

`A = C = 2*arctan(d_1/d_2)`

`B = D = 2*arctan(d_2/d_1)`

Height

`h=a*sin(A)=a*sin(B)`

Area

Area from the side and angles

`A_r=a^2*sin(A)=a^2*sin(B)`

Area from diagonals

`A_r=(d_1*d_2)/2`

Area from height and side

`A_r=a*h`

Perimeter

`P = 4*a`

Perimeter from diagonals

`P=2*sqrt(d_1^2+d_2^2)`

See also

Plane Geometry calculators
Geometry calculators
Mathematics calculators