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Areas
Trapezoidal Rule
Simpson's Rule
Other Methods
Coordinates
Example
Areas
This section of the Plane Surveying site discusses the derivation and use of different formulae for the the calculation of areas. To refer to these formulae while you are working in the problem solving areas of this site, please refer to the Areas section of the Formulae page. 
The following notes cover methods for determining the area of land parcels, either using data obtained from field survey measurements or information shown on existing maps and plans.
Uses of Area Calculations
The area of land parcels or regions is often needed as part of a volume calculation, for instance to determine the amount of fertilizer to be applied to a paddock or to determine runoff for stream flow analysis. The legal title description of a land allotment shows the area as well as the dimensions, for example:
Land parcels are not always contained by regular straight line or circular arc boundaries, especially when they front water courses or ridge lines. Methods for surveying these boundaries and computing the enclosed areas are as follows:
Irregular Areas
Trapezoidal Rule
Simpson's Rule
Other Methods
Polygons