Chapter 5: Applications of Integration
Section 5.7: Centroids
Example 5.7.5
Determine the centroid of the trapezoid 25 × 15 × 15 × 15 (feet), longest edge uppermost and horizontal.
Solution
Mathematical Solution
By the Pythagorean theorem and Figure 5.7.5(a), the height h of the trapezoid is .
With respect to Figure 5.7.5(a), let point be the origin of a Cartesian coordinate system. Then, the coordinates of points , are respectively,
The left and right edges of the trapezoid are given respectively by the equations
and
The area of the trapezoid is
Figure 5.7.5(a) 25 × 15 × 15 × 15 trapezoid
If is the centroid, then (by symmetry) and
= ≐ 7.66
Maple Solution
Initialize
Tools≻Load Package: Student Precalculus
Loading Student:-Precalculus
Define
Context Panel: Assign Name
Area of the trapezoid
Equations of the left and right edges
Apply the Line command from the Student Precalculus package.
Apply the formula from Table 5.7.1
=
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