Respuesta :

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

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

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:
[tex]base.edge= \frac{33}{3} [/tex]
[tex]base.edge=11[/tex]

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

The length of the base edge of regular triangular pyramid which has the slant height k=12 cm and lateral area AL = 198 cm2, is 11 cm.

What is the lateral area of a Regular triangular pyramid?

Lateral area of the cone is the area bounded by the surface of the regular triangular pyramid, and this Lateral area of the regular triangular pyramid can be found out using the following formula.

[tex]A_L=\dfrac{1}{2}(3a\times l)[/tex]

Here. (h) is the height of the pyramid and (l) is the slant height of it.

Regular triangular pyramid has,

  • The slant height k=12 cm.
  • Lateral area AL = 198 cm2.

Put the values in the above formula,

[tex]198=\dfrac{1}{2}(3a\times 12)\\a=\dfrac{198\times2}{3\times12}\\a=11\rm\; cm[/tex]

Thus, the length of the base edge of a regular triangular pyramid which has the slant height k=12 cm and lateral area AL = 198 cm2, is 11 cm.

Learn more about the lateral area here:

https://brainly.com/question/858717

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