To find the area of a regular hexagon with an apothem of 1.7 cm and a side length of 2 cm, we can follow these steps:
1. Determine the perimeter of the hexagon:
A regular hexagon has six sides of equal length. Given that each side length is 2 cm, the perimeter [tex]\( P \)[/tex] is calculated as:
[tex]\[
P = 6 \times \text{side length} = 6 \times 2 = 12 \, \text{cm}
\][/tex]
2. Calculate the area using the apothem and perimeter:
The formula for the area [tex]\( A \)[/tex] of a regular hexagon, using its apothem [tex]\( a \)[/tex] and perimeter [tex]\( P \)[/tex], is:
[tex]\[
A = \frac{1}{2} \times P \times a
\][/tex]
Plugging in the values for the perimeter and the apothem:
[tex]\[
A = \frac{1}{2} \times 12 \, \text{cm} \times 1.7 \, \text{cm}
\][/tex]
3. Simplify the expression to find the area:
Performing the multiplication:
[tex]\[
A = \frac{1}{2} \times 12 \times 1.7 = 6 \times 1.7 = 10.2 \, \text{cm}^2
\][/tex]
Therefore, the area of the regular hexagon is:
[tex]\[
10.2 \, \text{cm}^2
\][/tex]
