# Rhombus

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## 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
Ar : 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)