Question

How do I solve? Is the process for finding the area of a regular polygon the same for all shapes?

Answer 1

Given the information on the picture, we can find the apothem of the hexagon using the following formula:

$a=\sqrt[]{\frac{3}{4}s^2}$

in this case, we have the following:

$\begin{gathered} a=\sqrt[]{\frac{3}{4}(12)^2}=\sqrt[]{108}=10.4 \\ \Rightarrow a=10.4 \end{gathered}$

now that we have that the apothem is a = 10.4, we can find easily the perimeter by multiplying by 6 the measure of the side:

$P=6(12)=72\operatorname{cm}$

finally, now that we have the perimeter is P = 72 cm and the apothem, we can find the area of the hexagon:

$\begin{gathered} A=\frac{P\cdot a}{2} \\ \Rightarrow A=\frac{72(10.4)}{2}=374.4\operatorname{cm}^2 \end{gathered}$

therefore, the area of the hexagon is 374.4cm^2