Apothem

Geometry Level 2

Find the length of the apothem $A_p$ of a 12-sided regular polygon which side length is 12 cm.

Hint: Draw a triangle with the apothem and two contiguous vertices of the polygon and you´ll get this

Consider that $α$ is the central angle of the figure and $β$ is the internal angle.

6(2+\sqrt{3})

2(3-\sqrt{3})

6-\sqrt{3}

4(3+\sqrt{3})

6(2-\sqrt{3})

12-sin(15°)

1 solution

Sergio Melo
Jul 15, 2019

You can do it with $\frac{β}{2}$ if you want.