Question
Complete the steps to find the slant height, s, of the pyramid
Step 0 what we know
A side of the base of the pyramid is *blank 1* meters.
That means side b of the triangle must equal to *blank 2* meters.
Options for blank 1
A 6
B ?
C 10
5
Options for blank 2
A 10
B 6
C 12
D 5
Step 0 what we know
A side of the base of the pyramid is *blank 1* meters.
That means side b of the triangle must equal to *blank 2* meters.
Options for blank 1
A 6
B ?
C 10
5
Options for blank 2
A 10
B 6
C 12
D 5
Answers
Answered by
GPT-4o mini
To find the slant height \( s \) of a pyramid with a square base, we need to know the sides of the base and the height of the pyramid. However, the prompt does not mention the height of the pyramid or other required dimensions.
Assuming we are dealing with a square base and the base side is a certain length, we can derive the side \( b \) of the right triangle that helps us calculate the slant height \( s \).
### Step 0 what we know
1. A side of the base of the pyramid is **blank 1** meters.
2. That means side \( b \) of the triangle must equal to **blank 2** meters.
### Options for blank 1:
- A) 6
- B) ?
- C) 10
- D) 5
### Options for blank 2:
- A) 10
- B) 6
- C) 12
- D) 5
### To find \( b \):
If we're looking for the value of \( b \), we typically would define \( b \) as half the length of the base side (since it forms a right triangle where the line from the center of the pyramid base to a corner of the base forms half of the base side), plus the height of the pyramid if that value is given.
If we choose a base side length for *blank 1*, let's complete it with:
1. If we take option A (6 meters) for blank 1:
- The distance from the center of the base to one corner (which is \( b \)), would be:
\[
b = \frac{\text{side of base}}{2} = \frac{6}{2} = 3 \text{ meters.}
\]
- However, this specific value isn't among the options given for blank 2.
2. If we take option C (10 meters) for blank 1:
- \( b = \frac{10}{2} = 5 \text{ meters.}\)
This matches with option D (5 meters) being the value for blank 2.
3. If we take option D (5 meters) for blank 1:
- Then \( b = \frac{5}{2} = 2.5 \text{ meters.}\)
We can determine generally that, in a square pyramid:
- Choosing option C (10) for blank 1 results in:
- **Blank 1:** 10 meters
- **Blank 2:** 5 meters
This leads us to:
### Completion:
- A side of the base of the pyramid is **10** meters.
- That means side \( b \) of the triangle must equal to **5** meters.
Thus, the final answers are:
- **Blank 1:** C) 10
- **Blank 2:** D) 5
Assuming we are dealing with a square base and the base side is a certain length, we can derive the side \( b \) of the right triangle that helps us calculate the slant height \( s \).
### Step 0 what we know
1. A side of the base of the pyramid is **blank 1** meters.
2. That means side \( b \) of the triangle must equal to **blank 2** meters.
### Options for blank 1:
- A) 6
- B) ?
- C) 10
- D) 5
### Options for blank 2:
- A) 10
- B) 6
- C) 12
- D) 5
### To find \( b \):
If we're looking for the value of \( b \), we typically would define \( b \) as half the length of the base side (since it forms a right triangle where the line from the center of the pyramid base to a corner of the base forms half of the base side), plus the height of the pyramid if that value is given.
If we choose a base side length for *blank 1*, let's complete it with:
1. If we take option A (6 meters) for blank 1:
- The distance from the center of the base to one corner (which is \( b \)), would be:
\[
b = \frac{\text{side of base}}{2} = \frac{6}{2} = 3 \text{ meters.}
\]
- However, this specific value isn't among the options given for blank 2.
2. If we take option C (10 meters) for blank 1:
- \( b = \frac{10}{2} = 5 \text{ meters.}\)
This matches with option D (5 meters) being the value for blank 2.
3. If we take option D (5 meters) for blank 1:
- Then \( b = \frac{5}{2} = 2.5 \text{ meters.}\)
We can determine generally that, in a square pyramid:
- Choosing option C (10) for blank 1 results in:
- **Blank 1:** 10 meters
- **Blank 2:** 5 meters
This leads us to:
### Completion:
- A side of the base of the pyramid is **10** meters.
- That means side \( b \) of the triangle must equal to **5** meters.
Thus, the final answers are:
- **Blank 1:** C) 10
- **Blank 2:** D) 5