Question

If the surface area of a square pyrimd is 65ft² and the area of the four triangle faces is 40ft² what is the length of one of the sides?
25ft
21ft
6.25ft
5ft

Answer 1

To find the length of one side of the square pyramid, we can use the information about the surface area and the area of the triangular faces.

1. **Surface Area of the Pyramid**: The surface area \(S\) of a square pyramid can be expressed as:
\[
S = B + L
\]
where \(B\) is the area of the base and \(L\) is the total area of the triangular faces.

2. **Given Values**:
\[
S = 65 \, \text{ft}^2
\]
\[
L = 40 \, \text{ft}^2
\]

3. **Calculate the Area of the Base**:
\[
B = S - L = 65 \, \text{ft}^2 - 40 \, \text{ft}^2 = 25 \, \text{ft}^2
\]

4. **Area of the Base**: Since the base is a square, we denote the length of one side of the square as \(s\):
\[
B = s^2 \implies 25 \, \text{ft}^2 = s^2
\]

5. **Solving for \(s\)**:
\[
s = \sqrt{25 \, \text{ft}^2} = 5 \, \text{ft}
\]

Thus, the length of one of the sides of the square pyramid is **5 ft**.