A wooden pillar in the shape of a square prism has a base side length, [tex]s[/tex], of 4 inches and a height, [tex]h[/tex], of 9 inches. Find the surface area of the pillar using the formula [tex]SA = 2s^2 + 4sh[/tex].

A. 176 square inches
B. 208 square inches
C. 1,296 square inches
D. 2,448 square inches

To find the surface area of the wooden pillar, which is shaped like a square prism, we use the given formula for surface area: [tex]$ SA = 2s^2 + 4sh $[/tex].

Step-by-Step Solution:

1. Understand the Shape and Its Dimensions:
- The base of the prism is a square with side length [tex]$ s = 4 $[/tex] inches.
- The height of the prism is [tex]$ h = 9 $[/tex] inches.

2. Formula for Surface Area of a Square Prism:
The surface area (SA) of a square prism includes the area of the two square bases and the four rectangular sides. The formula is:
[tex]\[
SA = 2s^2 + 4sh
\][/tex]

3. Calculate the Area of the Two Square Bases:
- The area of one square base is [tex]$ s^2 = 4^2 = 16 $[/tex] square inches.
- Since there are two square bases, the total area of the bases is:
[tex]\[
2 \times s^2 = 2 \times 16 = 32 \text{ square inches}
\][/tex]

4. Calculate the Area of the Four Rectangular Sides:
- Each rectangular side has an area of [tex]$ s \times h = 4 \times 9 = 36 $[/tex] square inches.
- Since there are four identical rectangular sides, the total area of these sides is:
[tex]\[
4 \times (s \times h) = 4 \times 36 = 144 \text{ square inches}
\][/tex]

5. Add the Areas to Get the Total Surface Area:
- Combine the area of the two square bases and the four rectangular sides:
[tex]\[
SA = 32 + 144 = 176 \text{ square inches}
\][/tex]

Therefore, the surface area of the wooden pillar is 176 square inches.

The correct answer is A. 176 square inches.