1. Problem 5-a Locate the centroid of the plane area shown. y x 20 mm

2. Solving Problems on Your Own
Problem 5-a
20 mm
30 mm
Solving Problems on Your Own
Locate the centroid of the plane area shown.
36 mm
Several points should be emphasized when solving these types of problems.
24 mm x
1. Decide how to construct the given area from common shapes.
2. It is strongly recommended that you construct a table
containing areas or length and the respective coordinates of
the centroids.
3. When possible, use symmetry to help locate the centroid.

3. Decide how to construct the given area from common shapes.y
Problem 5-a Solution
Decide how to construct the given area from common shapes. C1 C2 30 x 10
Dimensions in mm

4. y
Problem 5-a Solution
Construct a table containing areas and respective coordinates of the centroids. C1 C2 30 x 10
Dimensions in mm
A, mm x, mm y, mm xA, mm yA, mm3
x 60 = , ,000
2 (1/2) x 30 x 36 = , ,440
S , ,440

5. XS A = S xA X (1740) = 28,200 X = 16.21 mm YS A = S yA
Problem 5-a Solution
Then
XS A = S xA
X (1740) = 28,200
X = mm C1 or C2
and
YS A = S yA 30
Y (1740) = 55,440 x 10
Y = 31.9 mm
Dimensions in mm or
A, mm x, mm y, mm xA, mm yA, mm3
x 60 = , ,000
2 (1/2) x 30 x 36 = , ,440
S , ,440