Perplexing Pentominoes

A pentomino is a shape that can be made using five different squares, with each square touching an entire side of another square. How many pentominoes are possible? Do all pentominoes have the same area? Do all pentominoes have the same perimeter? Examples of pentominoes are:

(Source: Mathematics Teaching in the Middle School, Sep-Oct 1994)

Extension
Are your findings the same if you work with hexominoes?