Area and perimeter of a parallelogram

A parallelepiped is a quadrangle the opposite edges of which are parallel and the same length; the adjacent sides do not form a right angle.
The diagonals are not the same length and perpendicular, but they halve one another.
The heights are the perpendicular distances between the opposite edges.

parallelogram

a, b	edge
d_1,2	diagonals
h_a	height to edge a
h_b	height to edge b
α_1,2	angle

Calculator

Select the units of measurement

Enter 3 values

edge

a =

edge

b =

height to edge a

h_a =

height to edge b

h_b =

diagonal

d₁ =

diagonal

d₂ =

angle

α₁ =

angle

α₂ =

area

A =

perimeter

P =

Error

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Calculation procedure

Formulas

parallelogram

area

$$ A = a\cdot h_a = b\cdot h_b $$

perimeter

$$ P = 2 \cdot (a + b) $$

height

$$ \begin{aligned} h_a &= b \cdot\sin\alpha_1 \\ \\ h_b &= a \cdot\sin\alpha_1 \end{aligned} $$

angle

$$ \begin{aligned} & \alpha_1 + \alpha_2 = 180\ ^\circ \\ \\ & \sin\alpha_1 = \sin\alpha_2 \end{aligned} $$

diagonal

$$ d_{1,2} = \sqrt{a^2 + b^2 - 2 \cdot a b \cdot\cos\alpha_{1,2}} $$

Area and perimeter of a parallelogram

parallelogram

Calculator

Select the units of measurement

Enter 3 values

edge

edge

height to edge a

height to edge b

diagonal

diagonal

angle

angle

area

perimeter

Error

Calculation procedure

Formulas

parallelogram

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