Question
What is the total surface area of the square pyramid?
mc016-1.jpg
48 square meters
64 square meters
76 square meters
88 square meters
mc016-1.jpg
48 square meters
64 square meters
76 square meters
88 square meters
Answers
GPT-4o mini
To calculate the total surface area of a square pyramid, we need to consider both the base and the four triangular sides.
The formula for the total surface area \( A \) of a square pyramid is:
\[
A = B + L
\]
Where:
- \( B \) is the area of the base
- \( L \) is the lateral surface area
1. **Area of the Base (B)**: This is simply the area of the square base. If the side length of the base is \( s \), then:
\[
B = s^2
\]
2. **Lateral Surface Area (L)**: This comprises the area of the four triangular sides. The area of one triangle can be found using:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
However, for the triangles of the pyramid, the base is equal to the side length \( s \) of the square, and we also need the slant height \( l \) of the triangles. Therefore, the total lateral surface area is given by:
\[
L = 4 \times \left(\frac{1}{2} \times s \times l\right) = 2sl
\]
So the total surface area \( A \) becomes:
\[
A = s^2 + 2sl
\]
To provide a specific numerical result, we need the lengths of \( s \) (the side of the base) and \( l \) (the slant height). Unfortunately, this information is not provided in your question. If you can provide the dimensions, I can calculate the exact surface area for you.
Otherwise, based on common options, it might involve guessing based on reasonable dimensions or estimating the values attached to the listed surface areas. If you have specific measurements for the pyramid, please share those to get an exact answer!
The formula for the total surface area \( A \) of a square pyramid is:
\[
A = B + L
\]
Where:
- \( B \) is the area of the base
- \( L \) is the lateral surface area
1. **Area of the Base (B)**: This is simply the area of the square base. If the side length of the base is \( s \), then:
\[
B = s^2
\]
2. **Lateral Surface Area (L)**: This comprises the area of the four triangular sides. The area of one triangle can be found using:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
However, for the triangles of the pyramid, the base is equal to the side length \( s \) of the square, and we also need the slant height \( l \) of the triangles. Therefore, the total lateral surface area is given by:
\[
L = 4 \times \left(\frac{1}{2} \times s \times l\right) = 2sl
\]
So the total surface area \( A \) becomes:
\[
A = s^2 + 2sl
\]
To provide a specific numerical result, we need the lengths of \( s \) (the side of the base) and \( l \) (the slant height). Unfortunately, this information is not provided in your question. If you can provide the dimensions, I can calculate the exact surface area for you.
Otherwise, based on common options, it might involve guessing based on reasonable dimensions or estimating the values attached to the listed surface areas. If you have specific measurements for the pyramid, please share those to get an exact answer!