Find the lateral area of a regular octagonal pyramid if the slant
height is 12 meters and the length of each side of its base is 6
meters

Hi again torrey2!!


The slant height is the diagonal distance from the apex of a regular
pyramid to the base. In other words, if we take one triangle of the
lateral sides of the pyramid, the slant height is the height of such
triangle:

"slant height of a regular pyramid: The altitude from the vertex on
any one of the triangular, lateral faces of the pyramid. It is
important to remember that the slant height is not the acutal height
of the pyramid itself; it is just the height of one of the triangles
that form a face of the pyramid."
From "Math "S" Terms":
http://www.themathlab.com/dictionary/swords/swords.htm


We know that for this regular octagonal pyramid we have eight
triangular lateral faces with the following dimensions:
Base = length of each side of the octagon = 6 m
Height = Slant height of the pyramid = 12 m

The area of each lateral face is:
L = 1/2 x Base x Height =  
  = 1/2 x 6 m x 12 m =
  = 36 m^2

We have eight triangular lateral faces, then:
S = 8 x 36 m^2 = 288 m^2


The lateral area of the regular octagonal pyramid is 288 m^2


I hope that this helps you.

Regards.
livioflores-ga