Question

Find the surface area of the regular hexagonal prism.
11 cm
4.3 cm
5 cm
Question content area bottom
Part 1
The surface area is
  
enter your response here cm Superscript 2.

Answer 1

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:

\[
\boxed{225 \text{ cm}^2}
\]