**Question 22:** **Solve for the area and the perimeter of the figure below:**  **Figure Description:** - The figure is a composite shape that consists of a larger rectangle with two smaller rectangles subtracted from its top corners. - The larger rectangle measures 20 inches in length and 10 inches in height. - Each of the two smaller rectangles on the top corners measures 5 inches in width and 6 inches in height. - Relevant dimensions are labeled as follows: - The total height of the larger rectangle is 10 inches. - The smaller rectangles are each 5 inches wide and extend 6 inches downward from the top. - The remaining height between the two smaller rectangles (inside height) is 4 inches (as the total height is 10 inches and the smaller rectangle is 6 inches). - The horizontal section between the two smaller rectangles at the top is 10 inches. **Steps to Solve:** 1. **Calculating the Area:** - First, calculate the area of the larger rectangle: \[ \text{Area}_{\text{larger}} = \text{Length} \times \text{Height} = 20\, \text{in} \times 10\, \text{in} = 200\, \text{sq in} \] - Next, calculate the area of one of the smaller rectangles: \[ \text{Area}_{\text{smaller}} = \text{Width} \times \text{Height} = 5\, \text{in} \times 6\, \text{in} = 30\, \text{sq in} \] - Since there are two identical smaller rectangles, the total area of the two smaller rectangles is: \[ \text{Total Area}_{\text{smaller}} = 2 \times 30\, \text{sq in} = 60\, \text{sq in} \] - Subtract the area of the two smaller rectangles from the area of the larger rectangle to obtain the area of the composite shape: \[ \text{Area}_{\text{composite}} = 200\, \text{sq in
**Question 22:** **Solve for the area and the perimeter of the figure below:**  **Figure Description:** - The figure is a composite shape that consists of a larger rectangle with two smaller rectangles subtracted from its top corners. - The larger rectangle measures 20 inches in length and 10 inches in height. - Each of the two smaller rectangles on the top corners measures 5 inches in width and 6 inches in height. - Relevant dimensions are labeled as follows: - The total height of the larger rectangle is 10 inches. - The smaller rectangles are each 5 inches wide and extend 6 inches downward from the top. - The remaining height between the two smaller rectangles (inside height) is 4 inches (as the total height is 10 inches and the smaller rectangle is 6 inches). - The horizontal section between the two smaller rectangles at the top is 10 inches. **Steps to Solve:** 1. **Calculating the Area:** - First, calculate the area of the larger rectangle: \[ \text{Area}_{\text{larger}} = \text{Length} \times \text{Height} = 20\, \text{in} \times 10\, \text{in} = 200\, \text{sq in} \] - Next, calculate the area of one of the smaller rectangles: \[ \text{Area}_{\text{smaller}} = \text{Width} \times \text{Height} = 5\, \text{in} \times 6\, \text{in} = 30\, \text{sq in} \] - Since there are two identical smaller rectangles, the total area of the two smaller rectangles is: \[ \text{Total Area}_{\text{smaller}} = 2 \times 30\, \text{sq in} = 60\, \text{sq in} \] - Subtract the area of the two smaller rectangles from the area of the larger rectangle to obtain the area of the composite shape: \[ \text{Area}_{\text{composite}} = 200\, \text{sq in
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Solve for the area and the perimeter of the figure below.
 <!-- Image source should be your own link or just a placeholder text, as per your actual use case -->
**Figure Description:**
- The figure is a composite shape that consists of a larger rectangle with two smaller rectangles subtracted from its top corners.
- The larger rectangle measures 20 inches in length and 10 inches in height.
- Each of the two smaller rectangles on the top corners measures 5 inches in width and 6 inches in height.
- Relevant dimensions are labeled as follows:
- The total height of the larger rectangle is 10 inches.
- The smaller rectangles are each 5 inches wide and extend 6 inches downward from the top.
- The remaining height between the two smaller rectangles (inside height) is 4 inches (as the total height is 10 inches and the smaller rectangle is 6 inches).
- The horizontal section between the two smaller rectangles at the top is 10 inches.
**Steps to Solve:**
1. **Calculating the Area:**
- First, calculate the area of the larger rectangle:
\[
\text{Area}_{\text{larger}} = \text{Length} \times \text{Height} = 20\, \text{in} \times 10\, \text{in} = 200\, \text{sq in}
\]
- Next, calculate the area of one of the smaller rectangles:
\[
\text{Area}_{\text{smaller}} = \text{Width} \times \text{Height} = 5\, \text{in} \times 6\, \text{in} = 30\, \text{sq in}
\]
- Since there are two identical smaller rectangles, the total area of the two smaller rectangles is:
\[
\text{Total Area}_{\text{smaller}} = 2 \times 30\, \text{sq in} = 60\, \text{sq in}
\]
- Subtract the area of the two smaller rectangles from the area of the larger rectangle to obtain the area of the composite shape:
\[
\text{Area}_{\text{composite}} = 200\, \text{sq in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F870e2c1d-d022-4f41-b5d2-13ea4c5e7ced%2F3a406088-31ef-4ae2-abed-74d4c569d7b5%2Fpll6mua.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 22:**
**Solve for the area and the perimeter of the figure below:**
 <!-- Image source should be your own link or just a placeholder text, as per your actual use case -->
**Figure Description:**
- The figure is a composite shape that consists of a larger rectangle with two smaller rectangles subtracted from its top corners.
- The larger rectangle measures 20 inches in length and 10 inches in height.
- Each of the two smaller rectangles on the top corners measures 5 inches in width and 6 inches in height.
- Relevant dimensions are labeled as follows:
- The total height of the larger rectangle is 10 inches.
- The smaller rectangles are each 5 inches wide and extend 6 inches downward from the top.
- The remaining height between the two smaller rectangles (inside height) is 4 inches (as the total height is 10 inches and the smaller rectangle is 6 inches).
- The horizontal section between the two smaller rectangles at the top is 10 inches.
**Steps to Solve:**
1. **Calculating the Area:**
- First, calculate the area of the larger rectangle:
\[
\text{Area}_{\text{larger}} = \text{Length} \times \text{Height} = 20\, \text{in} \times 10\, \text{in} = 200\, \text{sq in}
\]
- Next, calculate the area of one of the smaller rectangles:
\[
\text{Area}_{\text{smaller}} = \text{Width} \times \text{Height} = 5\, \text{in} \times 6\, \text{in} = 30\, \text{sq in}
\]
- Since there are two identical smaller rectangles, the total area of the two smaller rectangles is:
\[
\text{Total Area}_{\text{smaller}} = 2 \times 30\, \text{sq in} = 60\, \text{sq in}
\]
- Subtract the area of the two smaller rectangles from the area of the larger rectangle to obtain the area of the composite shape:
\[
\text{Area}_{\text{composite}} = 200\, \text{sq in
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