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
Related questions
Question
![**Lesson: Surface Area of Prisms and Cylinders**
### 12.2 Quick Check
**Question 6**
Find the surface area. Do not round your answer.
The image shows a hexagonal prism with the following dimensions:
- Height of the prism: 12 units
- Side length of the hexagonal base: 15 units
- Base area: 386.3 square units
The surface area of this prism can be calculated using the formula for the surface area of a prism, which is:
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Surface Area} \]
1. **Base Area**: Already given as 386.3 square units.
2. **Lateral Surface Area**: Can be calculated by multiplying the perimeter of the base by the height of the prism.
The formula for the perimeter \( P \) of a hexagon with side length \( a \) is:
\[ P = 6 \times a \]
Here, \( a = 15 \) units,
\[ P = 6 \times 15 = 90 \text{ units} \]
Now, the lateral surface area \( L \):
\[ L = \text{Perimeter} \times \text{Height} \]
\[ L = 90 \times 12 = 1080 \text{ square units} \]
Finally, the total surface area \( S \):
\[ S = 2 \times \text{Base Area} + \text{Lateral Surface Area} \]
\[ S = 2 \times 386.3 + 1080 = 772.6 + 1080 = 1852.6 \text{ square units} \]
The surface area is **1852.6 square units**.
**Answer:**
The surface area is \_\_\_\_\_\_ square units. (The blank should be filled with "1852.6").](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9a023c6-912c-46a5-9561-bfaf13c3fa3b%2F02ee4b60-04bd-4174-ae4f-e6a7cba74477%2F0xxktf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lesson: Surface Area of Prisms and Cylinders**
### 12.2 Quick Check
**Question 6**
Find the surface area. Do not round your answer.
The image shows a hexagonal prism with the following dimensions:
- Height of the prism: 12 units
- Side length of the hexagonal base: 15 units
- Base area: 386.3 square units
The surface area of this prism can be calculated using the formula for the surface area of a prism, which is:
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Surface Area} \]
1. **Base Area**: Already given as 386.3 square units.
2. **Lateral Surface Area**: Can be calculated by multiplying the perimeter of the base by the height of the prism.
The formula for the perimeter \( P \) of a hexagon with side length \( a \) is:
\[ P = 6 \times a \]
Here, \( a = 15 \) units,
\[ P = 6 \times 15 = 90 \text{ units} \]
Now, the lateral surface area \( L \):
\[ L = \text{Perimeter} \times \text{Height} \]
\[ L = 90 \times 12 = 1080 \text{ square units} \]
Finally, the total surface area \( S \):
\[ S = 2 \times \text{Base Area} + \text{Lateral Surface Area} \]
\[ S = 2 \times 386.3 + 1080 = 772.6 + 1080 = 1852.6 \text{ square units} \]
The surface area is **1852.6 square units**.
**Answer:**
The surface area is \_\_\_\_\_\_ square units. (The blank should be filled with "1852.6").
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