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.

Make it simple and shorter, like a 7th grader wrote it

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 four triangular sides.

**Step 1: Find the area of the base.**
The base is a square, and the area of a square is calculated using the formula:

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

The side length of the base is 12:

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

**Step 2: Find the area of one triangular side.**
The area of a triangle is given by the formula:

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

For the triangles, the base is the same as the side of the square, which is 12, and the height is the slant height, which is 18:

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

Calculating this gives:

\[
\text{Area of one triangle} = \frac{1}{2} \times 12 \times 18 = 6 \times 18 = 108
\]

**Step 3: Find the total area of the four triangular sides.**
Since there are four triangular sides, we multiply the area of one triangle by 4:

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

**Step 4: Calculate the total surface area.**
Now, we add the area of the base to the total area of the triangular sides:

\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of triangular sides}
\]
\[
\text{Total surface area} = 144 + 432 = 576
\]

So, the surface area of the square pyramid is **576 square units**.