Math Parallelogram

[pic] A parallelogram is a quadrilateral in which pairs of opposite sides are parallel and are congruent.
Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same)
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Name the kind of parallelogram this figure displays? Example 1: [pic]

|[pic] |A parallelogram with: |
| |all sides equal and |
| |angles "a" and "b" as right angles |
| |Is a square! |

Perimeter and area of a parallelogram

Perimeter of a parallelogram:

The perimeter can be calculated with the following formula:
[pic]
Where a and b are the side lengths.

Area of a parallelogram

The area can be calculated with the following formulas:

[pic]
Where b is the length of the base line, and h is the height of the parallelogram.

[pic]
Where a and b are the side lengths and θ is the angle.
[pic]

Example 2: Find the area and perimeter with the given length and side.
|a: |[pic] |Side length a |
|b: |[pic] |Side length b |
|h: |[pic] |Height |
|θ: |[pic] |Angle in degrees |

The perimeter is calculated:
[pic]
The area is calculated, using height and b:
[pic]
The area is calculated, using a, b and angle:
[pic]

Special parallelograms

If all angles are 900 degrees, then it is also called a rectangle.
If all angles are 900 degrees and the lines are of the same length, then it is also called a square.
If all sides are of the same length, then it is also called a rhombus.

Example 3: The sides of a 900 angle with the