7.6 Area 175
Now that you understand the significance of area in engineering analysis, let us look at its
units. The unit of area in SI is m
2. We can also use the multiples and the submultiples (see
Table 6.2) of SI fundamental units to form other appropriate units for area, such as mm
2
, cm
2
,
km
2
, and so on. Remember, the reason we use these units is to keep numbers manageable. The
common unit of area in the U.S. Customary system is ft
2
. Table 7.3 shows other units com-
monly used in engineering practice today and their equivalent values.
Area Calculations
The areas of common shapes, such as a triangle, a circle, and a rectangle, can be obtained using
the area formulas shown in Table 7.4. It is a common practice to refer to these simple areas as
primitive areas. Many composite surfaces with regular boundaries can be divided into primitive
areas. To determine the total area of a composite surface, such as the one shown in Figure 7.10,
we first divide the surface into the simpler primitive areas that make it up, and then we sum the
values of these areas to obtain the total area of the composite surface.
Examples of the more useful area formulas are shown in Table 7.4.Approximation of Planar Areas
There are many practical engineering problems that require calculation of planar areas of
irregular shapes. If the irregularities of the boundaries are such that they will not allow for the
irregular shape to be represented by a sum of primitive shapes, then we need to resort to an
approximation method. For these situations, you may approximate planar areas using any of the
procedures discussed next.The Trapezoidal Rule You can approximate the planar areas of an irregular shape with reason-
ably good accuracy using the trapezoidal rule. Consider the planar area shown in Figure 7.11.
To determine the total area of the shape shown in Figure 7.11, we use the trapezoidal approxi-
mation. We begin by dividing the total area into small trapezoids of equal heighth, as depicted
in Figure 7.11. We then sum the areas of the trapezoids. Thus, we begin with the equationAA 1 A 2 A 3 pAn (7.4)
TABLE 7.3 Units of Area and their Equivalent Values
Units of Area in Increasing Order Equivalent Value
1 mm
2
1 10
6
m
2
1 cm
2
1 10
4
m
2
100 mm
2
1 in
2
645.16 mm
2
1 ft
2
144 in
2
1 yd
2
9 ft
2
1 m
2
1.196 yd
2
1 acre 43,560 ft
2
1 km
2
1,000,000 m
2
247.1 acres
1 square mile 2.59 km2
640 acres
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