Question

surface area of a square pyramid is 160 cm^2 the area of the lateral triangles is 92 cm^2 what is length of one of the sides units

Answer 1

To find the length of one of the sides of the square pyramid, we need to understand a few components of the surface area and how they relate to one another.

The total surface area \( S \) of a square pyramid can be expressed as:

\[
S = \text{Base Area} + \text{Lateral Area}
\]

In your case, you have:

- Total Surface Area \( S = 160 \, \text{cm}^2 \)
- Lateral Area (area of the triangular faces) = \( 92 \, \text{cm}^2 \)

First, we can find the area of the base:

\[
\text{Base Area} = S - \text{Lateral Area} = 160 \, \text{cm}^2 - 92 \, \text{cm}^2 = 68 \, \text{cm}^2
\]

Since the base of the pyramid is a square, we can denote the length of one side of the square as \( s \). The area of the square base is given by:

\[
\text{Base Area} = s^2
\]

Setting this equal to the area we found:

\[
s^2 = 68 \, \text{cm}^2
\]

To find \( s \), we take the square root of both sides:

\[
s = \sqrt{68} \approx 8.246 \, \text{cm}
\]

Therefore, the length of one of the sides of the square pyramid is approximately \( 8.25 \, \text{cm} \).