Question

Find the area of a regular pentagon with a side 8 centimeters.


Please provide an explanation!

Answer 1

center angle = 360/8 = 45
half center angle = 22.5
tan half center angle = 4/altitude
so altitude = 4/.414 = 9.657
area of half of section = (1/2)(4)(9.657)
= 19.31
times 16 = 309

Answer 2

by the way if you want to do this exactly tan 22.5 = sqrt 2 - 1
because
tan (45/2) = [ 1- cos(45) ] / sin (45)
and cos (45) = sin (45) = 1/sqrt 2