Question

What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the triangular faces.

1. **Area of the Base**: The base is a square, so the area \( A_{\text{base}} \) can be calculated with the formula:
\[
A_{\text{base}} = \text{side}^2
\]
Given that the base edge is \( 1.5 \, \text{cm} \):
\[
A_{\text{base}} = (1.5 \, \text{cm})^2 = 2.25 \, \text{cm}^2
\]

2. **Area of the Triangular Faces**: There are 4 triangular faces on a square pyramid. The area of one triangular face \( A_{\text{triangle}} \) can be calculated with the formula:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base of each triangular face is the same as the edge of the square base (1.5 cm) and the height of each triangular face is the slant height (4 cm):
\[
A_{\text{triangle}} = \frac{1}{2} \times 1.5 \, \text{cm} \times 4 \, \text{cm} = \frac{1.5 \times 4}{2} = 3 \, \text{cm}^2
\]
Since there are 4 triangular faces:
\[
A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times 3 \, \text{cm}^2 = 12 \, \text{cm}^2
\]

3. **Total Surface Area**: Now, we can add the area of the base and the area of the triangular faces to get the total surface area \( A_{\text{total}} \):
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{triangles}} = 2.25 \, \text{cm}^2 + 12 \, \text{cm}^2 = 14.25 \, \text{cm}^2
\]

Rounding to the nearest whole number, the surface area of the square pyramid is:
\[
\boxed{14} \, \text{cm}^2
\]