# Parallelogram

## Definition

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

## Properties

1. Both pairs of opposite sides are equal; in ▱ABCD, AB = CD and BC = DA
2. Both pairs of opposite sides are parallel; so AB∥ CD and AD ∥ BC
3. Opposite angles are of equal measure; so ∠DAB = ∠BCD and ∠ABC = ∠CDA
4. Adjacent angles add up to 180°; ∠DAB +∠ABC = 180°, ∠ABC + ∠BCD = 180°, ∠BCD + ∠CDA = 180°, and ∠CDA + ∠DAB = 180°
5. 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:

Area (A) = b × h, here b = base, h = height

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 cm2
= 96 cm2

### Perimeter

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

Perimeter (P) = 2(a + b), here a & b are adjacent sides

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°)

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