How does a certain amount of lines make an area? If the lines have 0 width, shouldn't it take infinitely many lines? What's the mathematical proof of, say, the area of a square?
Consider a square with vertices A(0,0), B(1,0), C(1,1) and D(0,1). A random point inside the square is joined with (0,0) to get line segment AP. Another random point inside the square is joined with (1,0) to get line segment BQ. What is the probability that AP and BQ intersect?