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Find the centroid of the area for the given figure below
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| 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
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| Photo by Math Principles in Everyday Life |
Consider A1:
Area A1 = LW = (5 in)(2 in) = 10 in2
x1 = ½(5) = 2.5
y1 = ½(2) + 7 = 8
Therefore, C1(2.5, 8)
Consider A2:
Area A2 = LW = (3 in)(4 in) = 12 in2
x2 = ½(3) = 1.5
y2 = ½(4) + 3 = 5
Therefore, C2(1.5, 5)
Consider A3:
Area A3 = LW = (6 in)(3 in) = 18 in2
x3 = ½(6) = 3
y3 = ½(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").