Question

Determine the measures of the apothem, the radius, and the perimeter of the regular octagon.

a. a = 14.4, r = 15.6, p = 96
b. a = 14.4, r = 15.6, p = 12
c. a = 15.6, r = 14.4, p = 96
d. a = 10, r = 15.6, p = 96

Answer 1

a.) a = 14.4, r = 15.6, p = 96

Answer 2

the complete question in the attached figure

we know that
A) a regular Octagon has all its eight sides congruent
B) all the eight interior angles are also congruent
C) the measure of each angle = 135º
therefore
see the attached figure

∠ alfa=135°/2--------> 67.5°
AP=12/2---------> 6 units
cos (alfa)=AP/AO----------> AO=AP/cos (alfa)
AO=6/cos(67.5)---------> 15.68 units

the radius= distance AO----------> 15.68 units
radius=15.68 units
the apothem=distance OP

sin(alfa)=OP/AO---------> OP=sin(alfa)*AO
OP=sin(67.5°)*15.68-------> 14.49 units
the apothem=14.49 units

perimeter=12*8--------> 96 units
perimeter=96 units

the answers Part A), B) and C) are
apothem=14.49 units
radius=15.68 units
perimeter=96 units

therefore the option is the a.) a = 14.4, r = 15.6, p = 96