Areas of Standard Geometric Shapes

One of the most common applications of surveying is to measure the area of a lot, field, farm, or ranch. When a high level of accuracy is required, a professional engineer or a land surveyor should be employed. If this level of accuracy is not required, many areas can be determined with nothing more elaborate than a steel tape and the application of area formulas from geometry. The area of an irregularly shaped field can be found by subdividing it into standard shapes, determining the areas of the subdivisions by calculation, and then summing the areas of the subdivisions to find the total area. For example consider Figure 13.7.

There is no right or wrong way to divide the field. The goal is to collect the required measurements with the expenditure of the least amount of resources. The best way will depend on the equipment used and the obstacles that exist in the field.

Figure 13.8 shows two different ways to divide the irregular-shaped field into standard shapes. Either method will determine the area. Method B will probably take less time and resources because it will require fewer measurements. To use this method, it is necessary to apply the correct area formula for each common geometric shape. The next section will review the common shapes and the area formula for each.

FIGURE 13.8. Two alternatives for dividing irregular-shaped field into standard shapes.

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FIGURE 13.9. Triangle area with base and height known.

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