Answer:
[tex]\frac{27\sqrt[]{3}}{2}cm^2[/tex]
Explanation:
The polygon has 6 sides, therefore, it is a hexagon.
A regular hexagon is made up of 6 congruent equilateral triangles.
• Given that the length of the apothem of the hexagon = 3cm
,
• Therefore, the length of one side = 3cm
First, we find the height of one of the equilateral triangle:
[tex]\begin{gathered} 3^2=1.5^2+h^2 \\ h^2=3^2-1.5^2 \\ h^2=6.75 \\ h=\frac{3\sqrt[]{3}}{2}cm \end{gathered}[/tex]
Area of one equilateral triangle
[tex]\begin{gathered} =\frac{1}{2}\times3\times\frac{3\sqrt[]{3}}{2} \\ =\frac{9\sqrt[]{3}}{4}cm^2 \end{gathered}[/tex]
Therefore, the area of the polygon is:
[tex]\begin{gathered} =6\times\frac{9\sqrt[]{3}}{4} \\ =\frac{27\sqrt[]{3}}{2}cm^2 \end{gathered}[/tex]
