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Properties of a Trapezoid
Properties of a Right-Triangle
Properties of a Circular area
Properties of an Elliptical Area
All Geometric Shapes

Properties of a Parallelogram

- By Dr. Minas E. Lemonis, PhD - Updated: June 4, 2020

This tool calculates the basic geometric properties of a parallelogram. Enter below the shape dimensions. The calculated results will have the same units as your input. Please use consistent units for any input.

b =
h =
Additional input (select which):
Geometric properties:
Area =
Perimeter =
Lengths:
Side α =
Diagonal p =
Diagonal q =
Angles :
φ1 =
φ2 =
Centroid:
xc =
yc =
shape details

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Definitions

Geometry

Parallelogram is a quadrilateral shape with two pairs of parallel sides. The area of a parallelogram is given by the formulas:

A = b h

or

A = ab\sin{\varphi_1}

where a, b the lengths of the sides and h the height, perpendicular to b.

The perimeter of a parallelogram is simply the sum of the lengths of all sides:

P = 2\left(a+b\right)

The length of the left and right sides α, can be expressed in terms of the angle φ1, using the right triangle, with hypotenuse α (see figure below):

\alpha = \frac{h}{\sin{\varphi_1}}\\

shape geometry

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Interior angle φ2 is supplementary with φ1. Therefore:

\varphi_2 =180^{\circ} -\varphi_1

There are many ways to find the lengths of diagonals, once the sides or the interior angles are known. Here, a solution employing the Pythagorean Theorem on the highlighted right triangles (see next figure) is presented:

p = \sqrt{h^2 + \left(b+b_2\right)^2}

Similarly, the other diagonal is found as:

q = \sqrt{h^2 + \left(b-b_2\right)^2}

shape geometry

Centroid

The centroid of parallelogram coincides with the point where diagonals cross each other. Measuring from the left vertex of base, xc and yc distances are:

\begin{split} & x_{c} = 0.5\left(b+b_1\right)\\ & y_{c} = 0.5 h \end{split}

where A is the area of the trapezoid.

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See also
Properties of a Trapezoid
Properties of a Right-Triangle
Properties of a Circular area
Properties of an Elliptical Area
All Geometric Shapes