Amelia is decorating the outside of a box in the shape of a square pyramid. The figure below shows a net for the box. 5 m 3.7 m What is the surface area of the box, in square meters, that Amelia decorates?
Amelia is decorating the outside of a box in the shape of a square pyramid. The figure below shows a net for the box. 5 m 3.7 m What is the surface area of the box, in square meters, that Amelia decorates?
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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### Description of the Net
The net consists of:
- One square base with each side measuring 3.7 meters.
- Four triangular faces, each with a base of 3.7 meters and a slant height of 5 meters.
### Illustration
The diagram shows the net of a square pyramid, which is composed of a central square with four triangles attached to each side. The triangles fold up to meet at a single point above the center of the square, forming the pyramid.
### Dimensions
- The side length of the square base: **3.7 meters**
- The slant height of the triangular faces: **5 meters**
### Problem Statement
What is the surface area of the box, in square meters, that Amelia decorates?
### Solution:
To find the surface area of a square pyramid, we need to calculate the area of the square base and the area of the four triangular faces.
**Step 1: Calculate the area of the square base.**
\[ \text{Area of the square} = \text{side}^2 \]
\[ \text{Area of the square} = 3.7 \times 3.7 \]
\[ \text{Area of the square} = 13.69 \text{ square meters} \]
**Step 2: Calculate the area of one triangular face.**
\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area of one triangle} = \frac{1}{2} \times 3.7 \times 5 \]
\[ \text{Area of one triangle} = 9.25 \text{ square meters} \]
**Step 3: Calculate the total area of the four triangular faces.**
\[ \text{Total area of triangles} = 4 \times \text{Area of one triangle} \]
\[ \text{Total area of triangles} = 4 \times 9.25 \]
\[ \text{Total area of triangles} = 37 \text{ square meters} \]
**Step 4: Calculate the total](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71ad11dc-25a4-4aef-afaf-b0879e57e72d%2F6b9fae9e-c358-46a0-9721-055abe63d8d9%2F359xrrb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Calculating the Surface Area of a Square Pyramid**
Amelia is decorating the outside of a box in the shape of a square pyramid. The figure below shows a net for the box:
### Description of the Net
The net consists of:
- One square base with each side measuring 3.7 meters.
- Four triangular faces, each with a base of 3.7 meters and a slant height of 5 meters.
### Illustration
The diagram shows the net of a square pyramid, which is composed of a central square with four triangles attached to each side. The triangles fold up to meet at a single point above the center of the square, forming the pyramid.
### Dimensions
- The side length of the square base: **3.7 meters**
- The slant height of the triangular faces: **5 meters**
### Problem Statement
What is the surface area of the box, in square meters, that Amelia decorates?
### Solution:
To find the surface area of a square pyramid, we need to calculate the area of the square base and the area of the four triangular faces.
**Step 1: Calculate the area of the square base.**
\[ \text{Area of the square} = \text{side}^2 \]
\[ \text{Area of the square} = 3.7 \times 3.7 \]
\[ \text{Area of the square} = 13.69 \text{ square meters} \]
**Step 2: Calculate the area of one triangular face.**
\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area of one triangle} = \frac{1}{2} \times 3.7 \times 5 \]
\[ \text{Area of one triangle} = 9.25 \text{ square meters} \]
**Step 3: Calculate the total area of the four triangular faces.**
\[ \text{Total area of triangles} = 4 \times \text{Area of one triangle} \]
\[ \text{Total area of triangles} = 4 \times 9.25 \]
\[ \text{Total area of triangles} = 37 \text{ square meters} \]
**Step 4: Calculate the total
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