How to calculate the area of any irregular shape

Hi guyz!! actually i am making a sensor based project my goal is to calculate the area of any shape providedd to the machine........which sensor can i use for this project and how much will it cost give any ideas please.......

One option is image processing using a webcam and a PC. Sensor (webcam) can be obtained for <$10.

Go with what dougy said.
Though, could you explain a little about this? is it an existing machine that has some function? if so what?
Or is this a completely new machine you are designing?

Flat shape or 3D shape? The area or the volume?
I just wanted to make sure.

Yep, for 2D shapes just take a photo or scan of the shape and get the software to count "filled" pixels.

If it is going to be pages or photos, you can calculate it by getting a camera set at a fixed distance from the object to be scanned.
Let it take a picture and based on the picture it takes it determines the area. you need some way of outlining the area you want to calculate though.

For example, you can calibrate the machine by setting a piece of paper with known area onto it. and the pixel count will correspond to the area.
Use different known sizes ofcourse, and maybe the ratio of area to pixels will be the same. If it is, or roughly the same, you got yourself an area scanner