Question
Surface area of a square pyramid is 160cm^2. The area of the lateral triangles is 96cm^2. What is length of one of the sides. Units
Answers
GPT-4o mini
To find the length of one side of the square pyramid, we can use the relationship between the surface area, the lateral area, and the base area of the pyramid.
1. **Given**:
- Surface area of the pyramid = \( 160 \, \text{cm}^2 \)
- Area of the lateral triangles = \( 96 \, \text{cm}^2 \)
2. **Surface Area Formula**:
The total surface area of a square pyramid can be expressed as:
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]
3. **Base Area of a Square Pyramid**:
If \( s \) is the length of one side of the base (which is a square), the area of the base is:
\[
\text{Base Area} = s^2
\]
4. **Using the Information**:
It follows from our surface area formula:
\[
160 = s^2 + 96
\]
5. **Solving for the Base Area**:
Rearranging the equation gives:
\[
s^2 = 160 - 96 = 64
\]
6. **Finding the Side Length**:
To find \( s \):
\[
s = \sqrt{64} = 8 \, \text{cm}
\]
Therefore, the length of one of the sides of the square pyramid is \( \boxed{8 \, \text{cm}} \).
1. **Given**:
- Surface area of the pyramid = \( 160 \, \text{cm}^2 \)
- Area of the lateral triangles = \( 96 \, \text{cm}^2 \)
2. **Surface Area Formula**:
The total surface area of a square pyramid can be expressed as:
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
\]
3. **Base Area of a Square Pyramid**:
If \( s \) is the length of one side of the base (which is a square), the area of the base is:
\[
\text{Base Area} = s^2
\]
4. **Using the Information**:
It follows from our surface area formula:
\[
160 = s^2 + 96
\]
5. **Solving for the Base Area**:
Rearranging the equation gives:
\[
s^2 = 160 - 96 = 64
\]
6. **Finding the Side Length**:
To find \( s \):
\[
s = \sqrt{64} = 8 \, \text{cm}
\]
Therefore, the length of one of the sides of the square pyramid is \( \boxed{8 \, \text{cm}} \).