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 easy and simple

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 sides.

1. **Calculate the area of the base**:
The base of the square pyramid is a square, and the area of a square is given by the formula:

\[
\text{Area of base} = \text{side}^2
\]

The base length is 12, so:

\[
\text{Area of base} = 12^2 = 144
\]

2. **Calculate the area of the triangular sides**:
There are four triangular sides, and each triangle has a base equal to the side of the square (12) and a height equal to the slant height (18). The area of a triangle is given by the formula:

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

For one triangle:

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

Since there are four triangular sides, the total area of the triangles is:

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

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

\[
\text{Total Surface Area} = \text{Area of base} + \text{Total area of triangles}
\]
\[
\text{Total Surface Area} = 144 + 432 = 576
\]

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