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 hundredth.(1 poin

Answer 1

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

1. **Area of the base**:
The base of a square pyramid is a square. The area \( A_{\text{base}} \) of the base can be calculated using the formula:
\[
A_{\text{base}} = \text{side}^2
\]
Here, the side length is 1.5 cm.
\[
A_{\text{base}} = (1.5)^2 = 2.25 \, \text{cm}^2
\]

2. **Area of the triangular faces**:
Each triangular face has a base equal to the edge of the square (1.5 cm) and a height equal to the slant height of the pyramid (4 cm). The area \( A_{\text{triangle}} \) of one triangular face can be calculated using the formula:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here:
\[
A_{\text{triangle}} = \frac{1}{2} \times 1.5 \times 4 = \frac{6}{2} = 3 \, \text{cm}^2
\]

Since there are 4 triangular faces, the total area \( A_{\text{triangles}} \) is:
\[
A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times 3 = 12 \, \text{cm}^2
\]

3. **Total surface area**:
The total surface area \( A_{\text{total}} \) of the pyramid is the sum of the area of the base and the area of the triangular faces:
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{triangles}} = 2.25 + 12 = 14.25 \, \text{cm}^2
\]

Therefore, the surface area of the square pyramid is approximately **14.25 cm²** when rounded to the nearest hundredth.