Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Problem 4: Finding the Volume and Surface Area of a Right Triangular Prism
This exercise requires calculating the volume and surface area of a right triangular prism.
**Diagram Explanation:**
- The base of the prism is a right triangle with legs measuring 12 units and 15 units.
- The height of the prism is 20 units.
- Dotted lines indicate the right angle and internal dimensions.
**Volume Calculation:**
To find the volume of the prism, use the formula for the volume of a prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
1. **Calculate the area of the triangular base:**
\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 \times 15 = 90 \text{ square units} \]
2. **Calculate the volume:**
\[ \text{Volume} = 90 \times 20 = 1800 \text{ cubic units} \]
**Surface Area Calculation:**
The surface area of a prism is calculated by summing the areas of all its faces.
3. **Calculate the perimeter of the base:**
\[ 12 + 15 + \text{hypotenuse} \]
- Using Pythagorean Theorem, the hypotenuse \( h = \sqrt{12^2 + 15^2} = \sqrt{144 + 225} = \sqrt{369} \approx 19.21 \) units.
4. **Perimeter of the triangular base:**
\[ 12 + 15 + 19.21 \approx 46.21 \text{ units} \]
5. **Surface Area:**
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Perimeter} \times \text{Height} \]
\[ \text{Surface Area} = 2 \times 90 + 46.21 \times 20 \]
\[ \text{Surface Area} = 180 + 924.2 = 1104.2 \text{ square units} \]
Therefore:
- **Volume:** 1800 cubic units
- **Surface Area:** 1104.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4162ff7c-1449-44d3-b3e8-b87175535dd6%2F2ecf6198-5307-45c8-bd33-c70b118f33b6%2Fviuaho_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 4: Finding the Volume and Surface Area of a Right Triangular Prism
This exercise requires calculating the volume and surface area of a right triangular prism.
**Diagram Explanation:**
- The base of the prism is a right triangle with legs measuring 12 units and 15 units.
- The height of the prism is 20 units.
- Dotted lines indicate the right angle and internal dimensions.
**Volume Calculation:**
To find the volume of the prism, use the formula for the volume of a prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
1. **Calculate the area of the triangular base:**
\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 \times 15 = 90 \text{ square units} \]
2. **Calculate the volume:**
\[ \text{Volume} = 90 \times 20 = 1800 \text{ cubic units} \]
**Surface Area Calculation:**
The surface area of a prism is calculated by summing the areas of all its faces.
3. **Calculate the perimeter of the base:**
\[ 12 + 15 + \text{hypotenuse} \]
- Using Pythagorean Theorem, the hypotenuse \( h = \sqrt{12^2 + 15^2} = \sqrt{144 + 225} = \sqrt{369} \approx 19.21 \) units.
4. **Perimeter of the triangular base:**
\[ 12 + 15 + 19.21 \approx 46.21 \text{ units} \]
5. **Surface Area:**
\[ \text{Surface Area} = 2 \times \text{Base Area} + \text{Perimeter} \times \text{Height} \]
\[ \text{Surface Area} = 2 \times 90 + 46.21 \times 20 \]
\[ \text{Surface Area} = 180 + 924.2 = 1104.2 \text{ square units} \]
Therefore:
- **Volume:** 1800 cubic units
- **Surface Area:** 1104.
Expert Solution
Step 1
We can find the volume and surface area of the given right triangular prism in the below steps.
Step by step
Solved in 3 steps with 2 images
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