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

Keep it simple

Answer 1

To find the length of one of the sides of the square pyramid, we can use the information given about the surface area and the lateral area.

1. **Total Surface Area of the Pyramid (A)**: This is given as 160 cm².
2. **Lateral Area (LA)**: The area of the lateral triangles is given as 96 cm².

The total surface area of a square pyramid consists of the lateral area plus the area of the base (which is a square):

\[
A = LA + \text{Area of Base}
\]

We can rearrange this to find the area of the base:

\[
\text{Area of Base} = A - LA
\]

Substituting the known values:

\[
\text{Area of Base} = 160 \, \text{cm}^2 - 96 \, \text{cm}^2 = 64 \, \text{cm}^2
\]

Since the base of the pyramid is a square, we can express the area of the base as:

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

where \(s\) is the length of one side of the square base. Therefore, we can set up the equation:

\[
s^2 = 64 \, \text{cm}^2
\]

Taking the square root of both sides, we find:

\[
s = \sqrt{64} = 8 \, \text{cm}
\]

Thus, the length of one side of the square base is **8 cm**.