To find the surface area of a regular hexagonal prism, you can use the following formula:
\[ \text{Surface Area} = 2B + Ph \]
where:
- \( B \) is the area of the base (the hexagon),
- \( P \) is the perimeter of the base, and
- \( h \) is the height of the prism.
Step 1: Calculate the area of the hexagonal base \( B \)
A regular hexagon can be divided into 6 equilateral triangles. The area \( B \) of a regular hexagon with side length \( s \) is given by:
\[ B = \frac{3\sqrt{3}}{2} s^2 \]
Given that the side length of the hexagon is \( 4.3 \) cm:
\[ B = \frac{3\sqrt{3}}{2} (4.3)^2 \]
Calculating \( (4.3)^2 \):
\[ (4.3)^2 = 18.49 \]
So now we can find \( B \):
\[ B = \frac{3\sqrt{3}}{2} \times 18.49 \approx \frac{3 \times 1.732}{2} \times 18.49 \approx \frac{5.196}{2} \times 18.49 \approx 2.598 \times 18.49 \approx 48.00 \text{ cm}^2 \]
Step 2: Calculate the perimeter of the base \( P \)
The perimeter \( P \) of a regular hexagon is:
\[ P = 6s \]
For \( s = 4.3 \) cm:
\[ P = 6 \times 4.3 = 25.8 \text{ cm} \]
Step 3: Calculate the height \( h \)
The height \( h \) of the prism is given as \( 5 \) cm.
Step 4: Calculate the Surface Area
Now we can substitute \( B \), \( P \), and \( h \) into the surface area formula:
\[ \text{Surface Area} = 2B + Ph = 2 \times 48.00 + 25.8 \times 5 \]
Calculating both parts:
\[ 2B = 96.00 \text{ cm}^2 \] \[ Ph = 25.8 \times 5 = 129 \text{ cm}^2 \]
Adding both parts together:
\[ \text{Surface Area} = 96.00 + 129 = 225.00 \text{ cm}^2 \]
Final Answer
The surface area of the regular hexagonal prism is:
\[ \boxed{225 \text{ cm}^2} \]