Question

Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points)
solve in a easy simple form

Answer 1

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

### Step 1: Calculate the area of the base
The base of the square pyramid is a square with a side length of 12.

\[
\text{Area of the base} = \text{side} \times \text{side} = 12 \times 12 = 144
\]

### Step 2: Calculate the area of the triangular faces
Each triangular face has a base equal to the side length of the square (which is 12) and a height equal to the slant height (which is 18).

The area of one triangular face is given by:

\[
\text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the values:

\[
\text{Area of one triangle} = \frac{1}{2} \times 12 \times 18 = \frac{1}{2} \times 216 = 108
\]

Since there are 4 triangular faces, we multiply the area of one triangle by 4:

\[
\text{Total area of triangular faces} = 4 \times 108 = 432
\]

### Step 3: Calculate the total surface area
Finally, we can sum the area of the base and the total area of the triangular faces to find the surface area of the pyramid:

\[
\text{Total Surface Area} = \text{Area of the base} + \text{Total area of triangular faces}
\]

\[
\text{Total Surface Area} = 144 + 432 = 576
\]

### Conclusion
Thus, the surface area of the square pyramid is

\[
\boxed{576}
\]