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.
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Base Area: The base is a square, so the area \( A_{\text{base}} \) is given by: \[ A_{\text{base}} = \text{side}^2 = 3^2 = 9 \text{ in}^2. \]
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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: \[ A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times \frac{15}{2} = 30 \text{ in}^2. \]
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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.