Can you solve the pentomino challenge?

PART ONE

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Cut 5 one-inch squares from posterboard (or paper).

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Put the squares together, in such a way that they are joined at sides only.

The squares must join like this:

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They can't join like this:

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Also, the shapes are considered the same if they are mirrors.
In other words the two shapes below count as only one distinct shape.

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There are twelve shapes that can be made, see if you can find them all!


Solution to part one.

PART TWO

You should now have 12 shapes, each with an area of five square inches.
So all together the 12 shapes take up 60 square inches.

Now, the real challenge! Put the 12 shapes together in such a way that they
cover an area of 6 inches by 10 inches, like below:

Sound easy? It's not!
There are 2339 different ways to do it! Can you find just one??

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Solution to Part Two