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Find the centroid location (x, y) of the figure below.

Find the centroid location (x, y) of the figure below.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**DB Week 14 - Composite Bodies** **Objective:** Find the centroid location \((x, y)\) of the figure below. The image illustrates a composite body resembling a house shape, which is a combination of a rectangle and a triangle above it. The structure is symmetric about the vertical axis. **Key Dimensions:** - The overall width of the figure is \(300 \, \text{mm}\), divided equally into two sections of \(150 \, \text{mm}\) on either side of the central vertical axis. - The height of the rectangular section is \(400 \, \text{mm}\). - The total height of the composite figure is \(690 \, \text{mm}\), which includes the triangle on top. - The triangular section is \(240 \, \text{mm}\) high. - The rectangle inset in the middle is \(150 \, \text{mm}\) wide by \(400 \, \text{mm}\) high. - The unused border width all around the inset is \(50 \, \text{mm}\). **Graph/Diagram Description:** - The diagram is marked with axes labeled \(x'\) and \(y'\), indicating the original reference. - \(C\) denotes the centroid, which we need to locate. - Symmetrical guidelines vertically and horizontally assist in the analysis. This geometric combination challenges the understanding of centroid calculations in symmetric composite shapes.
Transcribed Image Text:**DB Week 14 - Composite Bodies** **Objective:** Find the centroid location \((x, y)\) of the figure below. The image illustrates a composite body resembling a house shape, which is a combination of a rectangle and a triangle above it. The structure is symmetric about the vertical axis. **Key Dimensions:** - The overall width of the figure is \(300 \, \text{mm}\), divided equally into two sections of \(150 \, \text{mm}\) on either side of the central vertical axis. - The height of the rectangular section is \(400 \, \text{mm}\). - The total height of the composite figure is \(690 \, \text{mm}\), which includes the triangle on top. - The triangular section is \(240 \, \text{mm}\) high. - The rectangle inset in the middle is \(150 \, \text{mm}\) wide by \(400 \, \text{mm}\) high. - The unused border width all around the inset is \(50 \, \text{mm}\). **Graph/Diagram Description:** - The diagram is marked with axes labeled \(x'\) and \(y'\), indicating the original reference. - \(C\) denotes the centroid, which we need to locate. - Symmetrical guidelines vertically and horizontally assist in the analysis. This geometric combination challenges the understanding of centroid calculations in symmetric composite shapes.
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