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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![### Surface Area of a Prism
**Problem Statement:**
What is the surface area of the prism shown below?
**Diagram Explanation:**
The image shows a triangular prism with the following dimensions:
- The base of the triangle is 8 inches.
- The height of the triangle is 11 inches.
- The length (depth) of the prism is 10 inches.
**Detailed Steps to Determine the Surface Area:**
1. **Identify the Shapes:**
- **Two Triangular Bases:**
- Base of each triangle (b) = 8 inches
- Height of each triangle (h) = 11 inches
- **Three Rectangular Lateral Faces:**
- The dimensions of these rectangles are determined by the sides of the triangular base and the length of the prism.
2. **Calculate the Area of the Triangular Bases:**
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \text{ in} \times 11 \text{ in} = 44 \text{ in}^2
\]
Since there are two triangular bases:
\[
\text{Total area of both triangles} = 2 \times 44 \text{ in}^2 = 88 \text{ in}^2
\]
3. **Calculate the Area of the Three Rectangular Faces:**
- **Face 1 (Rectangle with one side as the base of the triangle and the other as the length of the prism):**
\[
\text{Area} = \text{base} \times \text{length} = 8 \text{ in} \times 10 \text{ in} = 80 \text{ in}^2
\]
- **Face 2 and Face 3 (Rectangles with one side as each leg of the triangle and the other as the length of the prism):**
- Each triangle’s height as one leg (face) and prism length
\[
\text{Area of one triangular face along the length} = 11 \text{ in} \times 10 \text{ in} = 110 \text{ in}^2
\]
Since there are two such faces:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d1376b4-854f-4844-8630-994d3c61ce3e%2F525d0a2e-3c21-4165-ac15-060ab33252d0%2F8xzu21q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Surface Area of a Prism
**Problem Statement:**
What is the surface area of the prism shown below?
**Diagram Explanation:**
The image shows a triangular prism with the following dimensions:
- The base of the triangle is 8 inches.
- The height of the triangle is 11 inches.
- The length (depth) of the prism is 10 inches.
**Detailed Steps to Determine the Surface Area:**
1. **Identify the Shapes:**
- **Two Triangular Bases:**
- Base of each triangle (b) = 8 inches
- Height of each triangle (h) = 11 inches
- **Three Rectangular Lateral Faces:**
- The dimensions of these rectangles are determined by the sides of the triangular base and the length of the prism.
2. **Calculate the Area of the Triangular Bases:**
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \text{ in} \times 11 \text{ in} = 44 \text{ in}^2
\]
Since there are two triangular bases:
\[
\text{Total area of both triangles} = 2 \times 44 \text{ in}^2 = 88 \text{ in}^2
\]
3. **Calculate the Area of the Three Rectangular Faces:**
- **Face 1 (Rectangle with one side as the base of the triangle and the other as the length of the prism):**
\[
\text{Area} = \text{base} \times \text{length} = 8 \text{ in} \times 10 \text{ in} = 80 \text{ in}^2
\]
- **Face 2 and Face 3 (Rectangles with one side as each leg of the triangle and the other as the length of the prism):**
- Each triangle’s height as one leg (face) and prism length
\[
\text{Area of one triangular face along the length} = 11 \text{ in} \times 10 \text{ in} = 110 \text{ in}^2
\]
Since there are two such faces:
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