**Compute the coordinates of the centroid \((\bar{x}, \bar{y})\) of the area shown.**The diagram presents a composite shape, which is partly shaded. It features a quadrant of a circle integrated with a rectangle, marked by specific dimensions. The image includes two intersecting axes (\(x\) and \(y\)).### Diagram Details:- **Shapes**: The shape has both a straight and a curved boundary.- **Dimensions**: - \(a\), \(b\), and \(c\) are the horizontal measurements along the \(x\)-axis. - \(d\) is the vertical measurement along the \(y\)-axis.- **Reference**: The top-right corner contains a copyright notice by Michael Swanbom, dated 2013, indicating the image is licensed with Creative Commons (CC) under BY-NC-SA.### Measurement Values:- **Variable Table**: - \(a = 45 \, \text{mm}\) - \(b = 27 \, \text{mm}\) - \(c = 23 \, \text{mm}\) - \(d = 90 \, \text{mm}\)### Centroid Coordinates:- **\(x\) Coordinate of the Centroid**: \[ \bar{x} = \underline{\hspace{2cm}} \, \text{mm} \]- **\(y\) Coordinate of the Centroid**: \[ \bar{y} = \underline{\hspace{2cm}} \, \text{mm} \]**Note**: Ensure dimensions are accurate to facilitate the precise calculation of the centroid’s coordinates. The shape might not be shown to scale.

Answered: Image /qna-images/answer/6cb5bcb5-7419-48e2-939c-cf847ef3b5d8.jpg

Compute the coordinates of the centroid (x, y) of the area shown. a b | | a с d y Variable Value 45 mm 27 mm 23 mm 90 mm The coordinate of the centroid is 2013 Michael Swanbom Cc+❀O BY NC SA ·b*c* Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. d The y coordinate of the centroid is y C x mm. mm.

Compute the coordinates of the centroid (x, y) of the area shown. a b | | a с d y Variable Value 45 mm 27 mm 23 mm 90 mm The coordinate of the centroid is 2013 Michael Swanbom Cc+❀O BY NC SA ·bc Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. d The y coordinate of the centroid is y C x mm. mm.

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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Concept explainers

Length and Length related Variables

Length can de defined as the measurement or extent of physical quantities or objects from one terminal to another terminal. Stone age humans used finger length, step length, and so on to measure the size or displacement of an object. Nowadays, depending on how precise the measurement requires to be and the object’s size is measured, we use measuring devices for measurements like rulers and steel tape. Most people have used a ruler or tape measure to measure a particular distance or the size of an object. For more precise measurements of tiny objects, the development of measurement tools such as the Vernier caliper, which permits us to measure dimensions within 1/1000 of an inch. In the last few decades, electronic distance measuring instruments (EDMI) have been implemented that permit us to measure distances from a few feet to many miles with reasonable accuracy.

Question

**Compute the coordinates of the centroid \((\bar{x}, \bar{y})\) of the area shown.**

The diagram presents a composite shape, which is partly shaded. It features a quadrant of a circle integrated with a rectangle, marked by specific dimensions. The image includes two intersecting axes (\(x\) and \(y\)).

### Diagram Details:

- **Shapes**: The shape has both a straight and a curved boundary.
- **Dimensions**:
- \(a\), \(b\), and \(c\) are the horizontal measurements along the \(x\)-axis.
- \(d\) is the vertical measurement along the \(y\)-axis.
- **Reference**: The top-right corner contains a copyright notice by Michael Swanbom, dated 2013, indicating the image is licensed with Creative Commons (CC) under BY-NC-SA.

### Measurement Values:

- **Variable Table**:
- \(a = 45 \, \text{mm}\)
- \(b = 27 \, \text{mm}\)
- \(c = 23 \, \text{mm}\)
- \(d = 90 \, \text{mm}\)

### Centroid Coordinates:

- **\(x\) Coordinate of the Centroid**:
\[
\bar{x} = \underline{\hspace{2cm}} \, \text{mm}
\]

- **\(y\) Coordinate of the Centroid**:
\[
\bar{y} = \underline{\hspace{2cm}} \, \text{mm}
\]

**Note**: Ensure dimensions are accurate to facilitate the precise calculation of the centroid’s coordinates. The shape might not be shown to scale.

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