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Can you explain the strategy for winning this game with any target?

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Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Card Trick 2

Can you explain how this card trick works?

Threesomes

Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Can you draw triangles of area 1, 2, 3, ?.. square units?

Can you draw a triangle with an area of 1.5 square units?

What is the area of the smallest triangle you can draw? Is this triangle unique?

How many triangles of of area 2 square units can you draw and can you create "families" or "groups" of these triangles?