Arthur D. answered • 04/22/20
Forty Year Educator: Classroom, Summer School, Substitute, Tutor
draw a diagram
draw two radii
each radius is 16.2 in
draw the altitude (or apothem)
the apothem is perpendicular to one of the sides
you now have two right triangles which together make up one of the eight congruent triangles
the apothem bisects the central angle of 360/8=45°
the angle near the center of the polygon of either right triangle is 22.5°
use the sine function to find half of one side of the polygon
sin22.5°=x/16.2
0.3826834=x/16.2
x=16.2*0.3826834
x=6.199 in
the length of a side is 2*6.199
length of a side=12.398 in
now find the height or altitude (apothem)
use the cosine function
cos22.5°=a/16.2
0.923879=a/16.2
a=16.2*0.923879
a=14.9668 in
now you can find the area of the regular octagon
you can find the area of one triangle and multiply this area by eight or use the following formula:
A=(1/2)(apothem)(perimeter)
perimeter=8*12.398
perimeter=99.184 in
A=(1/2)(14.9668)(99.184)
A=742.23355 sq in
A=742 square inches
