To find the area of a regular hexagon with a side length of 8 cm and round it to the nearest tenth, we can use the well-known formula for the area of a regular hexagon. The formula is:
[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times \text{(side length)}^2 \][/tex]
Given that the side length is [tex]\( 8 \)[/tex] cm, we can substitute this into the formula:
Step 1: Substitute the side length into the formula.
[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times 8^2 \][/tex]
Step 2: Calculate [tex]\( 8^2 \)[/tex] first (which is [tex]\( 8 \times 8 \)[/tex]).
[tex]\[ 8^2 = 64 \][/tex]
Step 3: Multiply by [tex]\( \frac{3 \sqrt{3}}{2} \)[/tex].
[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \times 64 \][/tex]
Step 4: Calculate [tex]\( \frac{3 \sqrt{3}}{2} \)[/tex].
[tex]\[ \frac{3 \sqrt{3}}{2} \approx \frac{3 \times 1.732}{2} \approx \frac{5.196}{2} \approx 2.598 \][/tex]
Step 5: Multiply the result by 64.
[tex]\[ \text{Area} \approx 2.598 \times 64 \approx 166.272 \][/tex]
Step 6: Round the result to the nearest tenth.
[tex]\[ 166.272 \approx 166.3 \][/tex]
Therefore, the area of the regular hexagon with a side length of 8 cm, rounded to the nearest tenth, is approximately:
[tex]\[ \boxed{166.3 \text{ cm}^2} \][/tex]
