Area by counting dots
Click dots to make the corners of a shape, going round the shape in order, then press Close. The page counts the dots strictly inside (I) and the dots on the boundary (B), and Pick's formula gives the area with no measuring at all. Try to break it.
What's going on
Pick's theorem says that for any polygon whose corners sit on grid dots, Area = I + B/2 − 1. Interior dots count fully, boundary dots count half, and you give one back at the end.
The page checks it against a different method, the shoelace formula, which multiplies coordinates crosswise around the shape. The two always agree, which is more surprising the more wiggly your shape gets.
The rule needs a proper polygon: edges may not cross each other or double back along the same line, and there may not be holes. Draw a figure eight, or a "shape" whose corners all sit on one line, and the page will refuse. Extra corners that merely sit along a straight side are fine. Draw a shape with a hole and the formula misses by exactly one for each hole.
Sheet: Area by counting dots.