Question

Calculate da surface of da square pyramid dat has a base length of 12 and a slant height of 18 show ur work

Answer 1

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

1. **Area of the Base:**
The base of the pyramid is a square. The area \( A_{\text{base}} \) of a square is given by the formula:
\[
A_{\text{base}} = \text{side}^2
\]
Here, the length of the side of the square base is 12.
\[
A_{\text{base}} = 12^2 = 144
\]

2. **Area of the Triangular Faces:**
Each triangular face of the pyramid has a base equal to the side length of the square and a height equal to the slant height of the pyramid. 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, the base is 12 (the side length of the square) and the height is 18 (the slant height).
\[
A_{\text{triangle}} = \frac{1}{2} \times 12 \times 18 = \frac{1}{2} \times 216 = 108
\]

Since there are 4 triangular faces, the total area of the triangular faces \( A_{\text{triangular faces}} \) is:
\[
A_{\text{triangular faces}} = 4 \times A_{\text{triangle}} = 4 \times 108 = 432
\]

3. **Total Surface Area:**
Now, we can calculate the total surface area \( A_{\text{total}} \) of the pyramid by adding the area of the base and the area of the triangular faces:
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{triangular faces}}
\]
\[
A_{\text{total}} = 144 + 432 = 576
\]

Thus, the total surface area of the square pyramid is \( \boxed{576} \).