To solve this we are going to use the formula for the lateral surface area of a regular pyramid:
where
is the lateral surface area.
is the perimeter of the base.
is the slant height.
We know for our problem that
and
, so lets replace those values in our formula and solve for
:
Now we know that the perimeter of the base of our regular triangular pyramid is 33 cm. Remember that the perimeter of a triangle is the sum of its 3 sides. Since our pyramid is regular, its base will be an equilateral triangle, so to f<span>ind the length of the base edge, we just need to divide the perimeter by 3:
</span>
<span>
We can conclude that the length of the base edge of our regular triangular pyramid is
11 cm.</span>