## Definition

A parallelogram is a flat geometric shape having four sides with two pairs of opposite parallel sides that are equal in length.

## Properties

- Both pairs of opposite sides are equal; in ▱ABCD, AB = CD and BC = DA
- Both pairs of opposite sides are parallel; so AB∥ CD and AD ∥ BC
- The opposite angles are of equal measure; so ∠DAB = ∠BCD and ∠ABC = ∠CDA
- The adjacent angles add up to180°; ∠DAB +∠ABC = 180°, ∠ABC + ∠BCD = 180°, ∠BCD + ∠CDA = 180°, and ∠CDA + ∠DAB = 180°
- Diagonals bisect each other; here AC and BD bisect each other

## Formulas

### Area

The total space enclosed by the parallelogram. The formula is given below:

**Find the area of a parallelogram whose base is 8 cm and height is 12 cm.**

Solution:

As we know,

**Area (***A*) = *b* × *h*, here *b* = 8 cm and *h* =12 cm

= 8 x 12 cm^{2}

= 96 cm^{2}

### Perimeter

The total distance covered around the edge of the parallelogram. The formula is given below:

**Find the perimeter of the parallelogram whose two adjacent sides measure 11 m and 5 m.**

Solution:

As we know,

**Perimeter (***P*) = *2(a* + *b)*, here *a* = 11 m, *b* = 5 m, *c *= 11 m, and *d* = 5 m

=2(11 + 5) m

= 32 m

## Types

Based on their properties, parallelogram can be of three special types:

1. **Rhombus**

All sides equal.

No right angle

2. **Rectangle**

Two pairs of opposite sides equal

All four right angles (90°)

3. **Square**

All sides equal

All four right angles (90°)