# Parallelogram Formulas

Parallelogram is a quadrilateral with opposite sides that are parallel.

Properties of a Parallelogram:

• Opposite angles are equal.
• Opposite sides are of equal length.
• The sum of adjacent angles is 180 degrees.
• Diagonals bisect each other.
• The point of intersection of the diagonals is the center of symmetry of the parallelogram.

Special Cases of a Parallelogram:

• A parallelogram with all sides equal is called a rhombus.
• A parallelogram with all angles equal is called a rectangle.
• A parallelogram with all sides and all angles equal is called a square.

## Perimeter of a Parallelogram

$$C=2 \times (a+b)$$

where,

a, bā sides of the parallelogram.

## Area of a Parallelogram

$$S=a\times h$$

where,

aā base of the parallelogram.
hā height of the parallelogram.

When a = h, the area of such a parallelogram is equal to the area of the corresponding square (with side length a). This property was used by Euclid in the proof of the Pythagorean theorem in his book Elements.