Final answer:
The area of a regular hexagon with side lengths of 2 cm is approximately 10.4 cm², calculated using the formula (3\sqrt{3}/2) * s^2 and rounding the result to two significant figures.
Step-by-step explanation:
To find the area of a regular hexagon with side lengths of 2 cm, we can use the formula for the area of a regular polygon: A = (3\sqrt{3}/2)\times s^2, where s is the side length. In this case, s = 2 cm.
Substituting the given side length into the formula, we get:
A = (3\sqrt{3}/2)\times 2^2
A = (3\sqrt{3}/2)\times 4
A = 6\sqrt{3} cm2
Since \sqrt{3} is approximately 1.732, the area of the hexagon can be estimated as:
A \approx 6 \times 1.732 cm2
A \approx 10.392 cm2
Therefore, the approximate area of the hexagon is 10.4 cm2, when rounded to two significant figures.