Determine the x- and y-coordinates of the centroid of the shaded area. Ans. XY 4

Question

Determine the x- and y-coordinates of the centroid of the shaded area. Ans. XY 4.32 in 2"2" 1.25" 1.25" Problem 5/51 Be consistent with units Please explain. I have a big test tomorrow mornin Please handwrite and write quite legibly for everyone to read write very legibly and neatly so that it is easy to read out and understand Do not let the edges of a scanned or pictured image are cropped resulting illegible scripts Do not skip steps Never use the multiply symbol (s) between numbers and letters I need solutions and answers as soon as possible. Many thanks

Explanation / Answer

Using the symmetry we can see that the centroid must lie on the line ; y=x

lets divide the figure into three types

1 Circles = weight = area = Pi (1.25)^2

2. Bottom square = weight = 4*4

3. top rectangle = weight = 8*4

We will find their centriods and arrange them by weigth to get the centroid.

x = (bottom sq) + rectangle - circle

x= 2* 16 + ( 32- 3.925) 8+ ( 32- 3.925) *2 /(16+32-3.925 + 32-3.925)

x = 4.32 inch

similar for y

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