To determine the approximate area of a regular hexagon given its apothem and perimeter, we can use the formula for the area of a polygon:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{apothem} \times \text{perimeter} \][/tex]
Given in the problem:
- The apothem is [tex]\( 14 \text{ cm} \)[/tex].
- The perimeter is [tex]\( 96 \text{ cm} \)[/tex].
Now let's apply these values to the formula:
1. Write down the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{apothem} \times \text{perimeter} \][/tex]
2. Substitute the given values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times 14 \, \text{cm} \times 96 \, \text{cm} \][/tex]
3. Calculate the product of the apothem and the perimeter:
[tex]\[ 14 \, \text{cm} \times 96 \, \text{cm} = 1344 \, \text{cm}^2 \][/tex]
4. Multiply by [tex]\( \frac{1}{2} \)[/tex] to find the area:
[tex]\[ \text{Area} = \frac{1}{2} \times 1344 \, \text{cm}^2 = 672 \, \text{cm}^2 \][/tex]
Thus, the approximate area of the hexagon is [tex]\( 672 \, \text{cm}^2 \)[/tex].
The correct answer is therefore:
[tex]\[ 672 \, \text{cm}^2 \][/tex]
So the final answer is:
[tex]\[ \boxed{672 \, \text{cm}^2} \][/tex]
