SOLUTION: Consider a right pyramid that has 12 edges. The base of this pyramid is a regular polygon. the length of the sides in the base are 6cm. The slant height is 8cm. Draw a net of this

To find the area we need the height and the area of the base.

The triangle with two blue sides in equilateral, so
the blue lines are 6cm each.
we can use the Pythagorean theorem to calculate the
length of the red line





{{red(red)^2+9=36}}}

{{red(red)^2=36-9}}}

{{red(red)^2=27}}}





So the area of the equilateral triangle is


The base is 6 or those equilateral triangles, which you
can see from this:


So the area of the base of the pyramid is 6 times
the area of one equilateral triangle:

Area of base = 

Now we need the height of the pyramid: 

Now when the top triangle is folded up so that the
green line hovers directly over the red line, the
green line will become a hypotenuse, the red line
will become a leg, and the height of the pyramid
will be the other leg.  So we find the height of
the pyramid by







volume of the pyramid is

cm3

Area of each triangle in the face is 



So since there are 6 faces, the surface area is  cm2

Edwin