Question
A square pyramid and its net are shown below. What is the surface area of the pyramid?
17 cm
17 cm
< 15 cm .
C 15 cm..
16 cm
16 cm
5
17 cm
17 cm
< 15 cm .
C 15 cm..
16 cm
16 cm
5
Answers
GPT-4o mini
To find the surface area of the square pyramid, we can use the formula for the surface area of a pyramid, which is given by:
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]
1. **Calculate the Base Area**:
- The base of the pyramid is a square. If the side length of the square is \( s \), then the area of the base is:
\[
\text{Base Area} = s^2
\]
If we assume that the base has a side of \( 17 \, \text{cm} \):
\[
\text{Base Area} = 17 \times 17 = 289 \, \text{cm}^2
\]
2. **Calculate the Lateral Area**:
- The lateral area consists of four triangular faces. The area of one triangular face can be calculated as:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of each triangle is the same as the side length of the square base, \( 17 \, \text{cm} \). The height of the triangle (slant height) is needed for this calculation. If the slant height is \( l \), the area of one triangle would be:
\[
\text{Area of one triangle} = \frac{1}{2} \times 17 \times l
\]
Thus, the total lateral area (for 4 triangles) would be:
\[
\text{Lateral Area} = 4 \times \frac{1}{2} \times 17 \times l = 34l
\]
If we assume the height (slant height) \( l \) is \( 15 \, \text{cm} \):
\[
\text{Lateral Area} = 34 \times 15 = 510 \, \text{cm}^2
\]
3. **Total Surface Area**:
Now we can find the total surface area by adding the base area and the lateral area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} = 289 \, \text{cm}^2 + 510 \, \text{cm}^2 = 799 \, \text{cm}^2
\]
Thus, the surface area of the pyramid is \( 799 \, \text{cm}^2 \).
If you have different values for the base side length or slant height, please provide them for an accurate calculation!
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]
1. **Calculate the Base Area**:
- The base of the pyramid is a square. If the side length of the square is \( s \), then the area of the base is:
\[
\text{Base Area} = s^2
\]
If we assume that the base has a side of \( 17 \, \text{cm} \):
\[
\text{Base Area} = 17 \times 17 = 289 \, \text{cm}^2
\]
2. **Calculate the Lateral Area**:
- The lateral area consists of four triangular faces. The area of one triangular face can be calculated as:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of each triangle is the same as the side length of the square base, \( 17 \, \text{cm} \). The height of the triangle (slant height) is needed for this calculation. If the slant height is \( l \), the area of one triangle would be:
\[
\text{Area of one triangle} = \frac{1}{2} \times 17 \times l
\]
Thus, the total lateral area (for 4 triangles) would be:
\[
\text{Lateral Area} = 4 \times \frac{1}{2} \times 17 \times l = 34l
\]
If we assume the height (slant height) \( l \) is \( 15 \, \text{cm} \):
\[
\text{Lateral Area} = 34 \times 15 = 510 \, \text{cm}^2
\]
3. **Total Surface Area**:
Now we can find the total surface area by adding the base area and the lateral area:
\[
\text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} = 289 \, \text{cm}^2 + 510 \, \text{cm}^2 = 799 \, \text{cm}^2
\]
Thus, the surface area of the pyramid is \( 799 \, \text{cm}^2 \).
If you have different values for the base side length or slant height, please provide them for an accurate calculation!