Question

f the surface area of a square pyramid is 65 ft.2 and the areas of the four triangular faces is
40 ft.2, what is the length of one of the sides?
(1 point)
21 ft.
25 ft.
5 ft.
6.25 ft.

Answer 1

To find the length of one of the sides of the base of the square pyramid, we can use the formula for the surface area of a square pyramid:

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

We are given:
- The total surface area = 65 ft²
- The area of the four triangular faces (lateral area) = 40 ft²

Let \( B \) represent the area of the base. We can set up the equation:

\[
65 = B + 40
\]

Solving for \( B \):

\[
B = 65 - 40 = 25 \, \text{ft}^2
\]

Since the base of the pyramid is a square, we can denote the length of one side of the base as \( s \). Therefore, the area of the base can be expressed as:

\[
B = s^2
\]

This gives us the equation:

\[
s^2 = 25
\]

Taking the square root of both sides:

\[
s = \sqrt{25} = 5 \, \text{ft}
\]

Thus, the length of one of the sides of the base of the square pyramid is \( \boxed{5} \, \text{ft} \).