Verified Answer :

dalendrk

This polygon is a hexagon.

Triangle AED is equilateral triangle.

AH is the height of an equilateral triangle.

\(|AE|=|ED|=|DA|=a=5\\\\|AH|=\dfrac{a\sqrt3}{2}\\\\subtitute\\\\\boxed{|AH|=\dfrac{5\sqrt3}{2}}\)

InesWalston

Answer:

Length of the apothem is 4.33 units.

Step-by-step explanation:

The regular hexagon can be divided into 6 equal equilateral triangle.

So ΔAED is an equilateral triangle.

\(\Rightarrow m\angle A=60^{\circ}\)

In an equilateral triangle, the altitude bisects the angle, so

\(m\angle DAH=\dfrac{60}{2}=30^{\circ}\)

In ΔAHD,

\(\Rightarrow \cos 30=\dfrac{AH}{AD}\)

\(\Rightarrow \cos 30=\dfrac{AH}{5}\)

\(\Rightarrow AH=\cos 30\times {5}=\dfrac{\sqrt3}{2}\times 5=4.33\ units\)

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