Question
Surface area of a square pyramid is 160cm^2. Da area of da lateral triangles is 96cm^2. WUt is length of 1 of da sides. Units
Answers
GPT-4o mini
To find the length of one side of the square pyramid based on the given surface area and the area of the lateral triangles, we can follow these steps:
1. **Understanding the Surface Area**: The total surface area \( S \) of a square pyramid can be expressed as the sum of the area of the base and the area of the lateral faces (triangular sides).
\[
S = \text{Area of base} + \text{Area of lateral triangles}
\]
2. **Given Values**:
- Total surface area \( S = 160 \, \text{cm}^2 \)
- Area of lateral triangles = \( 96 \, \text{cm}^2 \)
3. **Finding the Area of the Base**: We can find the area of the base by rearranging the equation:
\[
\text{Area of base} = S - \text{Area of lateral triangles}
\]
\[
\text{Area of base} = 160 \, \text{cm}^2 - 96 \, \text{cm}^2 = 64 \, \text{cm}^2
\]
4. **Area of Base of a Square Pyramid**: The area of the base of a square pyramid is given by:
\[
\text{Area of base} = s^2
\]
where \( s \) is the length of one side of the base (which is a square). We now have:
\[
s^2 = 64 \, \text{cm}^2
\]
5. **Finding the Length of One Side**: Taking the square root of both sides gives:
\[
s = \sqrt{64} \, \text{cm} = 8 \, \text{cm}
\]
Therefore, the length of one side of the base of the square pyramid is **8 cm**.
1. **Understanding the Surface Area**: The total surface area \( S \) of a square pyramid can be expressed as the sum of the area of the base and the area of the lateral faces (triangular sides).
\[
S = \text{Area of base} + \text{Area of lateral triangles}
\]
2. **Given Values**:
- Total surface area \( S = 160 \, \text{cm}^2 \)
- Area of lateral triangles = \( 96 \, \text{cm}^2 \)
3. **Finding the Area of the Base**: We can find the area of the base by rearranging the equation:
\[
\text{Area of base} = S - \text{Area of lateral triangles}
\]
\[
\text{Area of base} = 160 \, \text{cm}^2 - 96 \, \text{cm}^2 = 64 \, \text{cm}^2
\]
4. **Area of Base of a Square Pyramid**: The area of the base of a square pyramid is given by:
\[
\text{Area of base} = s^2
\]
where \( s \) is the length of one side of the base (which is a square). We now have:
\[
s^2 = 64 \, \text{cm}^2
\]
5. **Finding the Length of One Side**: Taking the square root of both sides gives:
\[
s = \sqrt{64} \, \text{cm} = 8 \, \text{cm}
\]
Therefore, the length of one side of the base of the square pyramid is **8 cm**.