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Name: **Title: Understanding Composite Figures****Introduction:**Composite
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Description: **Title: Understanding Composite Figures****Introduction:**Composite figures arise in various geometry problems and are typically composed of more than one basic shape. In this lesson, we will analyze a figure composed of a rectangle and a semicircl

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Elementary Geometry For College Students, 7e

7th Edition

ISBN: 9781337614085

Author: Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher: Cengage,

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Question

**Title: Understanding Composite Figures**

**Introduction:**
Composite figures arise in various geometry problems and are typically composed of more than one basic shape. In this lesson, we will analyze a figure composed of a rectangle and a semicircle.

**Figure Explanation:**
The image depicts a composite figure consisting of:
1. A rectangle.
2. A semicircle positioned on top of the rectangle.

**Dimensions:**
- The rectangle has a height of $5$ units and a length of $12$ units.
- The semicircle is formed on the top length of the rectangle with a diameter equal to the length of the rectangle, $12$ units, which makes the radius $6$ units (since the radius is half of the diameter).

**Step-by-Step Guide to Find the Area of the Composite Figure:**

1. **Area of the Rectangle:**
\[
A_{\text{rectangle}} = \text{length} \times \text{height} = 12 \times 5 = 60 \text{ square units}
\]

2. **Area of the Semicircle:**
The area of a full circle with radius $r$ is given by:
\[
A_{\text{circle}} = \pi r^2
\]
Since we have a semicircle (half of a circle), the area will be:
\[
A_{\text{semicircle}} = \frac{1}{2} \pi r^2
\]
Substituting $r = 6$ units:
\[
A_{\text{semicircle}} = \frac{1}{2} \pi (6)^2 = \frac{1}{2} \pi (36) = 18 \pi \text{ square units}
\]

3. **Total Area of the Composite Figure:**
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 60 + 18\pi \text{ square units}
\]

**Conclusion:**
The composite figure's total area combines the area of the rectangle and the semicircle. Comprehending how to decompose and calculate the areas of these basic shapes forms the foundation for solving more complex geometrical problems.

Feel free to review the detailed breakdown if you need further clarification on any steps!

**Resources:

### Title: Understanding Area of Composite Figures

### Composite Figures

In geometry, a composite figure is a shape that is made up of two or more simple geometric shapes. Calculating the area of a composite figure involves breaking it down into simpler shapes whose area you can find individually, and then summing these areas together.

### Example Composite Figure

Below is a composite figure consisting of a rectangle and a triangle on top of it. The dimensions are labeled accordingly.

#### Diagram Description:
- The figure consists of a rectangle at the bottom and a triangle on top of the rectangle.
- The rectangle has a width of 10 units and a height of 6 units.
- The triangle has a base of 10 units, which is the same as the top width of the rectangle. The height of the triangle is 4 units.

#### Step-by-Step Calculation:

1. **Area of the Rectangle**:
- The area (A) is given by the formula:
$ A = \text{Width} \times \text{Height} $
- For the rectangle:
$ A_{\text{rectangle}} = 10 \times 6 = 60 \text{ square units} $

2. **Area of the Triangle**:
- The area (A) is given by the formula:
$ A = \frac{1}{2} \times \text{Base} \times \text{Height} $
- For the triangle:
$ A_{\text{triangle}} = \frac{1}{2} \times 10 \times 4 = 20 \text{ square units} $

3. **Total Area of the Composite Figure**:
- The total area is the sum of the areas of the rectangle and the triangle:
$ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} $
$ A_{\text{total}} = 60 + 20 = 80 \text{ square units} $

### Visual Guide:

The diagram shows a composite figure made up of a rectangle and a triangle. Key dimensions are labeled to guide you through calculating the areas of individual components and then summing them to find the total area of the composite figure.

This step-by-step process helps in visualizing how composite shapes can be broken down into fundamental shapes for easier calculation of their total area. By understanding and applying these principles, solving problems involving composite

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