If 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)

Answer 1

To find the length of one side of the square pyramid, let's first break down the information given:

1. Total surface area of the pyramid: \( S = 65 , \text{ft}^2 \)
2. Area of the four triangular faces: \( A_{\text{triangles}} = 40 , \text{ft}^2 \)

The surface area of a square pyramid can be calculated using the formula: \[ S = A_{\text{base}} + A_{\text{triangles}} \] where \( A_{\text{base}} \) is the area of the square base and \( A_{\text{triangles}} \) is the area of the four triangular faces.

Since the base of the pyramid is square, if we denote the length of one side of the base as \( s \), then the area of the base can be expressed as: \[ A_{\text{base}} = s^2 \]

Now, substituting the known values into the surface area equation: \[ 65 = s^2 + 40 \]

We can solve for \( s^2 \): \[ s^2 = 65 - 40 \] \[ s^2 = 25 \]

Now, taking the square root of both sides to find \( s \): \[ s = \sqrt{25} \] \[ s = 5 \]

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