To measure the area of an arbitrary two dimensional shape you will use a planimeter. To measure an area you could also just use a simple ruler depending on how big the area is.
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Pi (3.141...) is used for circles, and circles only. You use it to find the area and circumfrence.
-- Find out the population of the area. -- Find out the area of the area. -- Divide the population by the area. The result is the population density of the area.
Spectrometer
Pi is used to find the area and perimeter of a circle and the volume of a sphere, cylinder, and cone. Pi=3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196... That was 200 decimal places of Pi.