Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.1: Area And Initial Postulates
Problem 23E: A triangular corner of a store has been roped off to be used as an area for displaying Christmas...
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Question
- **Dimensions:**
- Width: 2 meters
- Height: 6 meters
- Depth: 2 meters
[Insert Text Box Here]
- **Answer:** [ __ ] m²
[Submit Answer Button]
**Explanation of the Diagram:**
The image shows a three-dimensional rectangular prism with the following dimensions:
- **Width:** 2 meters (as shown on the front face and extending along the horizontal base)
- **Height:** 6 meters (as shown on the vertical edge)
- **Depth:** 2 meters (shown along the side)
To find the surface area of the rectangular prism, we need to calculate the area of all six faces and sum them up:
The formula to find the surface area (SA) of a rectangular prism is:
\[ \text{SA} = 2lw + 2lh + 2wh \]
where:
- \( l \) = length (depth) = 2 meters
- \( w \) = width = 2 meters
- \( h \) = height = 6 meters
Thus,
\[ \text{SA} = 2(2 \times 2) + 2(2 \times 6) + 2(2 \times 6) \]
\[ \text{SA} = 2(4) + 2(12) + 2(12) \]
\[ \text{SA} = 8 + 24 + 24 \]
\[ \text{SA} = 56 \text{ m}^2 \]
Enter the surface area in the box provided and submit your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7b57b39-2401-4c71-9af3-0eb9f8912254%2Fa0cd8d22-a8a8-4cef-a2b8-71781a6e6051%2Fesendps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Surface Area of a Rectangular Prism
**Question:**
Find the surface area of the rectangular prism.
- **Dimensions:**
- Width: 2 meters
- Height: 6 meters
- Depth: 2 meters
[Insert Text Box Here]
- **Answer:** [ __ ] m²
[Submit Answer Button]
**Explanation of the Diagram:**
The image shows a three-dimensional rectangular prism with the following dimensions:
- **Width:** 2 meters (as shown on the front face and extending along the horizontal base)
- **Height:** 6 meters (as shown on the vertical edge)
- **Depth:** 2 meters (shown along the side)
To find the surface area of the rectangular prism, we need to calculate the area of all six faces and sum them up:
The formula to find the surface area (SA) of a rectangular prism is:
\[ \text{SA} = 2lw + 2lh + 2wh \]
where:
- \( l \) = length (depth) = 2 meters
- \( w \) = width = 2 meters
- \( h \) = height = 6 meters
Thus,
\[ \text{SA} = 2(2 \times 2) + 2(2 \times 6) + 2(2 \times 6) \]
\[ \text{SA} = 2(4) + 2(12) + 2(12) \]
\[ \text{SA} = 8 + 24 + 24 \]
\[ \text{SA} = 56 \text{ m}^2 \]
Enter the surface area in the box provided and submit your answer.
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