Question

Determine the surface area of a pyramid with a square base. The side of the square base is 3 in. and the slant height of the pyramid is 5 in.(1 point)
in.2

Answer 1

To determine the surface area of a pyramid with a square base, you need to calculate the area of the base and the area of the four triangular faces.

1. **Base Area**: The base is a square, so the area \( A_{\text{base}} \) is given by:
\[
A_{\text{base}} = \text{side}^2 = 3^2 = 9 \text{ in}^2.
\]

2. **Area of Triangular Faces**: Each triangular face has a base equal to the side of the square base and a height equal to the slant height. The area \( A_{\text{triangle}} \) of one triangular face can be calculated as:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 5 = \frac{15}{2} \text{ in}^2.
\]

Since there are four triangular faces, the total area for the triangular faces is:
\[
A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times \frac{15}{2} = 30 \text{ in}^2.
\]

3. **Total Surface Area**: The total surface area \( A_{\text{total}} \) of the pyramid is the sum of the base area and the area of the triangular faces:
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{triangles}} = 9 + 30 = 39 \text{ in}^2.
\]

Thus, the surface area of the pyramid is \( \boxed{39} \) in².