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