# Parallelogram Calculator

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Lets first understand, what is a parallelogram and how we can find different properties of a parallelogram?

Parallelogram

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

The 3-D counterpart of a parallelogram is a parallelopiped.

Characterizations

1. A parallelogram has two pairs of opposite sides are parallel.

2. A parallelogram has two pairs of opposite sides are equal in length.

3. A parallelogram has two pairs of opposite angles are equal in measure.

4. Diagonals of a parallelogram bisect each other.

5. Adjacent angles of a parallelogram are supplementary.

6. Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.

7. The sum of the squares of the sides of the parallelogram equals the sum of the squares of its diagonals.

8. A parallelogram has rotational symmetry of order 2.

9. The sum of the distances from any interior point of a parallelogram to the sides of the parallelogram is independent of the location of the point.

Properties of a parallelogram

1. Opposite sides of a parallelogram are parallel.

2. The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

3. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.

4. Any line through the midpoint of a parallelogram bisects the area.

5. A parallelogram cannot be inscribed in any triangle with less than twice its area.

6. The diagonals of a parallelogram divide it into four triangles of equal area.

Formulas

Let the Base of the Parallelogram be \(B\) units,

and the Height of the Parallelogram be \(H\) units.

Area of the Parallelogram will be \(BH\) square units.

Let the Adjacent Sides of the Parallelogram be \(A\) and \(B\) units respectively,

and the Angle between the Adjacent Sides of the Parallelogram be \(\theta \).

Perimeter of the Parallelogram will be \(2(A + B)\) units.

Area of the Parallelogram will be \(AB\sin\theta \) square units.

For calculating different properties of the parallelogram using above parallelogram calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.