Approximately how much material is needed to make the tent illustrated in the following figure (both ends and the bottom should be included)? 6 11 511
Approximately how much material is needed to make the tent illustrated in the following figure (both ends and the bottom should be included)? 6 11 511
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
4. Approximately how much material is needed to make the tent illustrated in the following figure (both ends and the bottom should be included)?
**Description of the Figure:**
The figure depicts a triangular prism-shaped tent with two triangular sides and three rectangular sections. The dimensions are as follows:
- Each triangular side has a height of 6 ft and a base of 5 ft.
- The rectangular sides are formed by extending the 5 ft base with a height of 3 ft.
**Solution Steps:**
1. **Calculate the area of the triangular sides:**
- Formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
- For two triangles:
\[ \text{Total Area of triangles} = 2 \times \left(\frac{1}{2} \times 5 \, \text{ft} \times 6 \, \text{ft}\right) = 2 \times 15 \, \text{sq ft} = 30 \, \text{sq ft} \]
2. **Calculate the area of the rectangular base:**
- Dimensions are 5 ft by 11 ft.
- \[ \text{Area} = 5 \, \text{ft} \times 11 \, \text{ft} = 55 \, \text{sq ft} \]
3. **Calculate the area of the two rectangular sides:**
- Each side is 3 ft high and extends along the 11 ft length.
- \[ \text{Area of one side} = 3 \, \text{ft} \times 11 \, \text{ft} = 33 \, \text{sq ft} \]
- \[ \text{Total for both sides} = 2 \times 33 \, \text{sq ft} = 66 \, \text{sq ft} \]
4. **Total material needed:**
- Sum the areas of all parts:
\[ \text{Total Area} = 30 \, \text{sq ft} + 55 \, \text{sq ft} + 66 \, \text{sq ft} = 151 \, \text{sq ft} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79d4d229-649f-4192-a00b-385a235528b8%2Fe0ad9e1e-412e-4473-ba80-14f0dd852eb2%2Fkipd06n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
4. Approximately how much material is needed to make the tent illustrated in the following figure (both ends and the bottom should be included)?
**Description of the Figure:**
The figure depicts a triangular prism-shaped tent with two triangular sides and three rectangular sections. The dimensions are as follows:
- Each triangular side has a height of 6 ft and a base of 5 ft.
- The rectangular sides are formed by extending the 5 ft base with a height of 3 ft.
**Solution Steps:**
1. **Calculate the area of the triangular sides:**
- Formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
- For two triangles:
\[ \text{Total Area of triangles} = 2 \times \left(\frac{1}{2} \times 5 \, \text{ft} \times 6 \, \text{ft}\right) = 2 \times 15 \, \text{sq ft} = 30 \, \text{sq ft} \]
2. **Calculate the area of the rectangular base:**
- Dimensions are 5 ft by 11 ft.
- \[ \text{Area} = 5 \, \text{ft} \times 11 \, \text{ft} = 55 \, \text{sq ft} \]
3. **Calculate the area of the two rectangular sides:**
- Each side is 3 ft high and extends along the 11 ft length.
- \[ \text{Area of one side} = 3 \, \text{ft} \times 11 \, \text{ft} = 33 \, \text{sq ft} \]
- \[ \text{Total for both sides} = 2 \times 33 \, \text{sq ft} = 66 \, \text{sq ft} \]
4. **Total material needed:**
- Sum the areas of all parts:
\[ \text{Total Area} = 30 \, \text{sq ft} + 55 \, \text{sq ft} + 66 \, \text{sq ft} = 151 \, \text{sq ft} \
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