## Monday, March 25, 2013

### Centroid - Area

Category: Physics, Mechanics

"Published in Newark, California, USA"

Find the centroid of the area for the given figure below

 Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

 Photo by Math Principles in Everyday Life

Put the given figure above in x and y axis and assign the origin at the lower left corner of the figure. Divide the given figure into three rectangles and assign their center. Label further the given figure above, we have

 Photo by Math Principles in Everyday Life

Consider A1:

Area A1 = LW = (5 in)(2 in) = 10 in2
x1 = ½(5) = 2.5
y1½(2) + 7 = 8
Therefore, C1(2.5, 8)

Consider A2:

Area A2 = LW = (3 in)(4 in) = 12 in2
x2½(3) = 1.5
y2½(4) + 3 = 5
Therefore, C2(1.5, 5)

Consider A3:

Area A3 = LW = (6 in)(3 in) = 18 in2
x3½(6) = 3
y3½(3) = 1.5
Therefore, C3(3, 1.5)

Area AT = A1 + A2 + A3
= 10 in2 + 12 in2 + 18 in2
= 40 in2

Now, we can get the coordinates of the Centroid of the given figure. Let's get the x value of the Centroid as follows

Let's get the y value of the Centroid as follows

Therefore, the coordinates of the Centroid is (2.425", 4.175").