For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Figures can be described in this way: $(p, i)$. For example, the red square has a $(p,i)$ of $(4,0)$, the grey triangle $(3,1)$, the green triangle $(5,0)$ and the blue shape $(6,4)$:
Each figure you produce will always enclose an area ($A$) of the square dotty paper.
The examples in the diagram have areas of $1$, $1 {1 \over 2}$, and $6$ sq units.
Do you agree?
Draw more figures; tabulate the information about their perimeter points ($p$), interior points ($i$) and their areas ($A$).
Can you find a relationship between all these three variables ($p$, $i$ and $A$)?
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