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the arm is sliding. Both dθ and dm are arbitrarily small, and reflect the rotation of the scale in a plane perpendicular to the tracing arm.

Figure 3.4: Area Calculation (Kunkle, 2001)

The area of the pentagon BCEC’B’ can be expressed as the sum of area BCE and area EC’B’B as shown in Equation 3.1. The area of BCE is that of a triangle, while area EC’B’B is that of a rectangle. As mentioned earlier, k is the length of the tracing arm.

dw = area(BCEC' B') dw = area(BCE) + area(EC' B' B)

Equation 3.1

dw = 1 k 2 dθ + kdm 2

The region traced by the tracing arm is determined by integrating Equation 3.1. The formula for W, as shown in Equation 3.2, describes the area of the entire region EC’B’B.

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