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
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
