Question

20pts

Answer 1

This polygon is a hexagon.

Triangle AED is equilateral triangle.

AH is the height of an equilateral triangle.

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

Answer 2

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,

$\Rightarrow \cos 30=\dfrac{AH}{AD}$

$\Rightarrow \cos 30=\dfrac{AH}{5}$

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