Respuesta :

dalendrk
This polygon is a hexagon.

Triangle AED is equilateral triangle.

AH is the height of an equilateral triangle.

[tex]|AE|=|ED|=|DA|=a=5\\\\|AH|=\dfrac{a\sqrt3}{2}\\\\subtitute\\\\\boxed{|AH|=\dfrac{5\sqrt3}{2}}[/tex]
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.

[tex]\Rightarrow m\angle A=60^{\circ}[/tex]

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

[tex]m\angle DAH=\dfrac{60}{2}=30^{\circ}[/tex]

In ΔAHD,

[tex]\Rightarrow \cos 30=\dfrac{AH}{AD}[/tex]

[tex]\Rightarrow \cos 30=\dfrac{AH}{5}[/tex]

[tex]\Rightarrow AH=\cos 30\times {5}=\dfrac{\sqrt3}{2}\times 5=4.33\ units[/tex]