Question

a regular octagon has perimeter 112. what is the area of the octagon?

Answer 1

each side (say A) =112/8=14
as octagon hence 8 triangle will made inside octagon,if you join each vertices to the center of octagon.
angle made at each triangle at octagon center is = 360/8=45
as both base angle of each triangle will same in octagon=(180-45)/2=67.5
area of one triangle is= (1/2)*14*height ; height=7 * tan (67.5)=16.8994
area of one triangle= 7 * 16.8994=118.29
area of octagon =8 * area of each triangle=8 ( 118.29 )=946.37 ans