Writing my comment idea in more detail: Lets say you have your image input to your application as a black and white pixel array, for example something like:
Then each black pixel can be represented with a 1 and each empty white pixel represented with a 0. The corresponding array would look like:
\begin{array}{c c}
0 & 0 & 1 & 1 & 0 & 0 & 0\\
0 & 1 & 0 & 0 & 1 & 1 & 0\\
1 & 0 & 0 & 0 & 0 & 0 & 1\\
1 & 0 & 0 & 0 & 0 & 0 & 1\\
0 & 1 & 0 & 0 & 1 & 1 & 0\\
0 & 0 & 1 & 1 & 0 & 0 & 0\\
\end{array}
Once you have this you can just loop through the two dimensional array and find the approximate area by counting the number of white pixels inside the drawn object. Obviously in with an image with much finer detail the array becomes larger but I think the same idea will work. Even an image that is $1000\times{}1000$ pixels will still only contain 1 million entries and only a fraction of them would be ones. The perimeter is even easer as you simple have to count the number of black pixels.
In terms of whether this is a "good" project I can only say that I am glad that I don't have to do it. I think the vast majority of the work you will have to put in to it is going to be in user interface design. How we go from a piece of paper to a filtered image where my algorithm suggestion will work is going to be the hard part. Then again maybe this is for a UI class? Any ways good luck.
