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)
Write it like a human and show the explanation and equation and make it short sentences

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 is a square. The formula for the area of a square is:
\[
\text{Area of the base} = \text{side}^2
\]
Given the base length is 12, we have:
\[
\text{Area of the base} = 12^2 = 144
\]

**Step 2: Calculate the area of the triangular faces.**
There are four triangular faces. The area of one triangle can be calculated using the formula:
\[
\text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of each triangle is the same as the side length of the square base (12), and the height is the slant height (18). Thus:
\[
\text{Area of one triangle} = \frac{1}{2} \times 12 \times 18 = \frac{1}{2} \times 216 = 108
\]
Since there are four triangles, we multiply the area of one triangle by 4:
\[
\text{Total area of triangles} = 4 \times 108 = 432
\]

**Step 3: Calculate the total surface area.**
Now, we can find the total surface area by adding the area of the base and the total area of the triangular faces:
\[
\text{Total Surface Area} = \text{Area of the base} + \text{Total area of triangles}
\]
\[
\text{Total Surface Area} = 144 + 432 = 576
\]

**Final Answer:**
The surface area of the square pyramid is **576 square units**.