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

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 find the length of the base edge, we just need to divide the perimeter by 3:



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

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