Centroid of composite area (one question)

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SUMMARY

The discussion centers on calculating the centroid of a composite area, specifically addressing confusion regarding the components of the formula used in the textbook. The numerator includes the product (1)(6)(2), representing the width, total length, and height of a skinny rectangle. Additionally, the term 2[3.5(3)(1)] is clarified, where 3.5 denotes the y-distance of the centroid of the skinny rectangles from the x-axis, while 3 and 1 represent their length and width, respectively. Understanding these components is crucial for accurately determining the centroid in composite area calculations.

PREREQUISITES
  • Understanding of composite area calculations
  • Familiarity with centroid concepts in geometry
  • Basic knowledge of rectangle dimensions and properties
  • Ability to interpret mathematical formulas and notation
NEXT STEPS
  • Study the principles of calculating centroids for various geometric shapes
  • Learn about the application of the centroid in structural engineering
  • Explore advanced topics in composite area analysis
  • Review examples of centroid calculations in textbooks or online resources
USEFUL FOR

Students studying geometry, engineers involved in structural design, and anyone interested in understanding the principles of centroid calculations in composite areas.

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I was doing this example from my textbook and looked at the solution guide. I'm confused as to where the textbook got a certain number.

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In the numerator of their work, they got (1)(6)(2), which I'm assuming is the width of the skinny rectangle, the total length of the bottom section, and the height of the bottom rectangle, respectively...correct me if I'm wrong.

The next part is 2[3.5(3)(1)]

The 2 outside the square bracket is for the two smaller rectangles poking up, the 3 would be the length of them, and the 1 would be the width of them. But what is that 3.5?

Sorry for cutting off the denominator from the picture, but I understand that part. It's just that 3.5 that I'm unsure of.

Thanks!
 
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The 3.5 is the y-distance of the centroid of the skinny rectangles from the x axis.
 
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