Use integration to determine the x coordinate(and only the x coord.) of the centriod of the shape(s) shown

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Use integration to determine the x coordinate(and only the x coord.) of the centriod of the shape(s) shown

The diagram represents a trapezoid graphed on a coordinate plane with axes labeled \( X \) and \( Y \).

**Description of the Trapezoid:**

- **Orientation:** The trapezoid is positioned horizontally.
- **Dimensions:**
  - The left side of the trapezoid is 6 inches long and is parallel to the \( Y \)-axis.
  - The top side is 4 inches long and lies parallel to the \( X \)-axis.
  - The bottom side is 12 inches long, running along the \( X \)-axis.
  - The right side of the trapezoid is slanted, creating the trapezoid shape.
- **Position:**
  - The leftmost vertical side starts at the origin of the axes (0,0) and rises up to 6 inches along the \( Y \)-axis.
  - The top horizontal side begins 2 inches along the \( X \)-axis and runs until 6 inches along the \( X \)-axis.

The diagram illustrates the configuration of a trapezoid defined by its dimensions on a coordinate plane, useful for exploring geometric properties and calculations such as area or perimeter.
Transcribed Image Text:The diagram represents a trapezoid graphed on a coordinate plane with axes labeled \( X \) and \( Y \). **Description of the Trapezoid:** - **Orientation:** The trapezoid is positioned horizontally. - **Dimensions:** - The left side of the trapezoid is 6 inches long and is parallel to the \( Y \)-axis. - The top side is 4 inches long and lies parallel to the \( X \)-axis. - The bottom side is 12 inches long, running along the \( X \)-axis. - The right side of the trapezoid is slanted, creating the trapezoid shape. - **Position:** - The leftmost vertical side starts at the origin of the axes (0,0) and rises up to 6 inches along the \( Y \)-axis. - The top horizontal side begins 2 inches along the \( X \)-axis and runs until 6 inches along the \( X \)-axis. The diagram illustrates the configuration of a trapezoid defined by its dimensions on a coordinate plane, useful for exploring geometric properties and calculations such as area or perimeter.
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