**Problem 9-64:****Task:** Locate the centroid (\( \bar{x}, \bar{y} \)) of the shaded area.**Diagram Explanation:**The diagram shows a composite shape that is composed of a right triangle, a rectangle, and a semicircle. Here are the key measurements and features:- **Right Triangle (Left Section):** - Base: 3 inches - Height: 1 inch- **Rectangle (Middle Section):** - Width: 3 inches - Height: 1 inch- **Semicircle (Right Section):** - Radius: 3 inches - Center aligns with the right edge of the rectangleThe shape is symmetric about the \( y \)-axis, with axes shown as coordinates \( x \) and \( y \), and the semicircle oriented such that its flat side aligns with the top edge of the rectangle and triangle. The task is to determine the location of the centroid for this composite shape.

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Answered: 4. Locate the centroid (7, 5) of the…

Engineering

Civil Engineering

4. Locate the centroid (7, 5) of the shaded area. 1 in, 3 in. - 3 in.- -3 in.- Prob. 9-64

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

**Problem 9-64:**

**Task:** Locate the centroid (\( \bar{x}, \bar{y} \)) of the shaded area.

**Diagram Explanation:**

The diagram shows a composite shape that is composed of a right triangle, a rectangle, and a semicircle. Here are the key measurements and features:

- **Right Triangle (Left Section):**
- Base: 3 inches
- Height: 1 inch

- **Rectangle (Middle Section):**
- Width: 3 inches
- Height: 1 inch

- **Semicircle (Right Section):**
- Radius: 3 inches
- Center aligns with the right edge of the rectangle

The shape is symmetric about the \( y \)-axis, with axes shown as coordinates \( x \) and \( y \), and the semicircle oriented such that its flat side aligns with the top edge of the rectangle and triangle. The task is to determine the location of the centroid for this composite shape.

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