Question
What is the total surface area of the square pyramid below?
A square pyramid. The square base has side lengths of 6 meters. The triangular sides have a height of 8 meters.
132 m2
144 m2
160 m2
228 m2
A square pyramid. The square base has side lengths of 6 meters. The triangular sides have a height of 8 meters.
132 m2
144 m2
160 m2
228 m2
Answers
GPT-4o mini
To find the total surface area of the square pyramid, we need to calculate the area of the square base and the area of the triangular sides (lateral surface area) separately, and then add them together.
1. **Area of the square base:**
The base is a square with side length \( s = 6 \) meters.
\[
\text{Area of the base} = s^2 = 6^2 = 36 \, \text{m}^2
\]
2. **Area of the triangular sides:**
The pyramid has 4 triangular faces. Each triangular face has a base of 6 meters (the length of the side of the square base) and a height of 8 meters.
The area of one triangular face is given by the formula:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24 \, \text{m}^2
\]
Since there are 4 triangular faces:
\[
\text{Total area of the triangular sides} = 4 \times 24 = 96 \, \text{m}^2
\]
3. **Total surface area of the pyramid:**
Now we can calculate the total surface area by adding the area of the base and the area of the triangular sides:
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of the triangular sides} = 36 \, \text{m}^2 + 96 \, \text{m}^2 = 132 \, \text{m}^2
\]
Thus, the total surface area of the square pyramid is **132 m²**.
1. **Area of the square base:**
The base is a square with side length \( s = 6 \) meters.
\[
\text{Area of the base} = s^2 = 6^2 = 36 \, \text{m}^2
\]
2. **Area of the triangular sides:**
The pyramid has 4 triangular faces. Each triangular face has a base of 6 meters (the length of the side of the square base) and a height of 8 meters.
The area of one triangular face is given by the formula:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24 \, \text{m}^2
\]
Since there are 4 triangular faces:
\[
\text{Total area of the triangular sides} = 4 \times 24 = 96 \, \text{m}^2
\]
3. **Total surface area of the pyramid:**
Now we can calculate the total surface area by adding the area of the base and the area of the triangular sides:
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of the triangular sides} = 36 \, \text{m}^2 + 96 \, \text{m}^2 = 132 \, \text{m}^2
\]
Thus, the total surface area of the square pyramid is **132 m²**.