A pyramid has a slant height of 6 meters. If its base is a regular
octagon with sides that measure 4 meters, find the lateral area of the
pyramid.

Hi there,

The first thing you need to do is find the height of one of faces that
make up the pyramid. Each face is a triangle, so to find its height
you need to take the 4m base of the triangle and bisect it giving you
a point 2m from each side. From that point you can draw a line up to
the apex of the pyramid. Once you have this line, you can use the
Pythagorean theorem (a^2+b^2=c^2) to find the height of the triangle.

h^2=6^2-2^2
h^2=36-4
h^2=32
h=sqrt32

Now that you have the height of one of the faces you can use the
formula for the area of a triangle (base*height)/2 to find the area of
one of the faces of the pyramid. Multiply the area of the face by 8
and you will get the lateral area of the pyramid.

area=[(4*sqrt32)/2]*8
    =90.50966799

I hope this answers your question! If you have any questions or are
unclear about anything please feel free to ask for clarification.

Regards,
Deadlychiapet