Question

Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.

Answer 1

The answer is 11 cm Hope this helps 

Answer 2

To solve this we are going to use the formula for the lateral surface area of a regular pyramid: $LSA= \frac{1}{2} pk$
where 
$LSA$ is the lateral surface area.
$p$ is the perimeter of the base.
$k$ is the slant height.

We know for our problem that $LSA=198$ and $k=12$, so lets replace those values in our formula and solve for $p$:
$LSA= \frac{1}{2} pk$
$198= \frac{1}{2} (p)(12)$
$198=6p$
$p= \frac{198}{6}$
$p=33$

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 find the length of the base edge, we just need to divide the perimeter by 3:
$base.edge= \frac{33}{3}$
$base.edge=11$

We can conclude that the length of the base edge of our regular triangular pyramid is 11 cm.