How do i find the apothem of a decagon with the radius of

A.  13.31'  to the nearest hundredth.

B.  86.52' to the nearest hundredth.

Step-by-step explanation:

Part A>

The apotherm of a regular polygon is the distance of the line segment from the centre of the polygon to the midpoint of a side.

2 radii of this decagon joined to the endpoints of a side form an isosceles triangle with equal sides = 14 cm.

The apotherm is the altitude of this triangle.  The  vertex of the triangle  has an angle of 360 / 10 = 36 degrees and the apotherm bisects this angle.

So using trigonometry on the right triangle formed:

cos 18 = x / 14   where x is the apotherm.

x = 14 cos 18

=  13.31'  (answer).

Part B.

Using trigonometry on the right triangle again:

sin 18 = x/2 / 14     (where x is the length of a side of the hexagon)

x/2 = 14 sin 18

x = 2 * 14 sin 18

= 8.652'.

As a decagon has 10 sides the perimeter = 8.652 * 10

= 86.52' to the nearest hundredth.

your answer would be 10x - 1

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.