SketchandCalc.com allows users to draw any shape, either freehand or by grid, on a simple grid and calculate both its area and perimeter. More generally, math sites such as SmartConversion.com and Calculator.net have facilities to calculate the area of several common 2-D shapes.
SketchandCalc also allows users to import maps or images, making it a very flexible tool for calculating area. It is not a 3-D modelling package, though, so it only offers area and perimeter, not volume. It is a paid-for service, but users can get one set of results for free, as of November 2015, by sharing the website's details on social media.