Introduction
1. One of the main purposes of your topographical survey may be to determine the area of a tract of land where you want to build a fish-farm. From existing topographical maps, you may need to calculate the area of a watershed or of a future reservoir (see Water, Volume 4 in this series).
Note: in land surveying, you should regard land areas as horizontal surfaces, not as the actual area of the ground surface. You always measurehorizontal distances.
2. You will often need to know the areas of cross-section profiles to calculate the amount of earthwork you need to do.
Horizontal area
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 Cross-section area
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3. You may determine areas either directly from field measurements, or indirectly, from a plan or map. In the first case, you will find all the measurements of distances and angles you need by surveying, and you will calculate the areas from them. In the second case, you will draw a plan or map first (see Chapter 9). Then you will get the dimensions you need from the scale, and determine the area on that basis.
4. There are several simple methods available for measuring areas. Some of these are graphic methods, where you compare the plan or map of the area you need to measure to a drawn pattern of known unit sizes. Others are geometric methods, where you use simple mathematical formulas to calculate areas of regular geometrical figures, such as triangles, trapeziums*, or areas bounded by an irregular curve.
Note: a trapezium is a four-sided polygon with two parallel sides.
5. The simple methods will be described in detail in the next sections. They are also summarized in Table 13.
Triangle
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Trapezium 1
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Trapezium 2
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Irregular area
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TABLE 13
Simple area measurement methods
Section
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Method
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Remarks
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| 10.2 | Strips | Graphic method giving rough estimate |
| 10.3 | Square-grid | Graphic method giving good to very good estimates |
| 10.4 | Subdivision into regular geometric figures such as, triangles, trapeziums | Geometric method giving good to very good estimates |
| 10.5 | Trapezoidal rule | Geometric method giving good to very good estimates Suitable for curved boundary |
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10.2 How to use the strips method for measuring areas
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1. Get a piece of transparent paper, such as tracing paper or light-weight square-ruled millimetric paper. Its size will depend on the size of the mapped area you need to measure.
2. On this paper, draw a series of strips, by drawing a series of parallel lines at a regular, fixed interval. Choose this strip width W to represent a certain number of metres. You can follow the scale of the plan or map to do this. | |
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Example
Scale 1: 2 000; strip width W = 1 cm = 20 m.
Scale 1: 50 000; strip width W = 1 cm = 500 m.
Note: the smaller the strip width, the more accurate your estimate of the land area will be.
3. Place the sheet of transparent paper over the plan or map of the area you need to measure, and attach it securely with drawing pins or transparent tape. | |
Scale: 1: 2.000
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4. For each strip, measure the distance AB in centimetres along a central line between the boundaries of the area shown on the map.
5. Calculate the sum of these distances in centimetres. Then, according to the scale you are using, multiply to find the equivalent distance in the field, in metres. | |
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Example
Scale is 1 :2000 and 1 cm = 20 m.
Sum of distances = 16 cm.
Equivalent ground distance: 16 x 20 m = 320 m. | |
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6. Multiply this sum of real distances (in metres) by the equivalent width of the strip W (in metres) to obtain a rough estimate of the total area in square metres.
Example
Sum of equivalent distances is 320 m.
Strip width (1 cm) is equivalent to 20 m.
Land area: 320 m x 20 m = 6 400 m2 or 0.64 ha
Note: 10000 m2 = 1 hectare (ha)
7. Repeat this procedure at least once to check on your calculations. | |
Total area = 320 m x 20 m = 6400 m2
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