1 Answer

Derek O · Answer 1 · 2023-11-02T06:48:26+0000

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

$a=\sqrt[]{(3)/(4)s^2}$

in this case, we have the following:

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

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:

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

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

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