Question

determine the surface area of a pyramid with a square base. The side of the javascript:void(0)square base is 3in. and the slant height of the pyramid is 5in

Answer 1

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

1. **Calculate the area of the square base:**
\[
\text{Area of the base} = \text{side}^2 = 3 \, \text{in} \times 3 \, \text{in} = 9 \, \text{in}^2
\]

2. **Calculate the area of one triangular face:**
The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For each triangular face of the pyramid, the base is equal to the side of the square base (3 in), and the height is the slant height (5 in):
\[
A_{\text{triangle}} = \frac{1}{2} \times 3 \, \text{in} \times 5 \, \text{in} = \frac{15}{2} \, \text{in}^2 = 7.5 \, \text{in}^2
\]

3. **Calculate the total area of the four triangular faces:**
\[
\text{Total area of triangles} = 4 \times A_{\text{triangle}} = 4 \times 7.5 \, \text{in}^2 = 30 \, \text{in}^2
\]

4. **Calculate the total surface area of the pyramid:**
\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of triangles}
\]
\[
\text{Total surface area} = 9 \, \text{in}^2 + 30 \, \text{in}^2 = 39 \, \text{in}^2
\]

Therefore, the surface area of the pyramid is \( \boxed{39 \, \text{in}^2} \).