Question

Find the perimeter of a triangular – based pyramid with slant height 18m and lateral surface area 360${m^2}$.

Answer 1

Hint: In this particular question use the concept that the lateral surface area of a regular pyramid is equal to the half times the product of perimeter of a triangular based pyramid and the slant height of the pyramid, so use this concept to reach the solution of the question.

Complete step-by-step answer:
The pictorial representation of a triangular based pyramid is shown above.
Given data:
Slant height of the pyramid = 18 m.
Let slant height be denoted by L.
Therefore, L = 18 m.
It is also given that the lateral surface area of a triangular – based pyramid = 360 ${m^2}$.
Let it be denoted by L.S.A.
Therefore, L.S.A = 360 ${m^2}$.
Let the perimeter of a triangular – based pyramid be P meters.
Now as we all know that the lateral surface area of a regular pyramid is equal to the half times the product of perimeter of a triangular based pyramid and the slant height of the pyramid.
Therefore, L.S.A = $\dfrac{1}{2}\left( {P \times L} \right)$ square meters.
Now substitute the values in the above equation we have,
$ \Rightarrow $360 = $\dfrac{1}{2}\left( {P \times 18} \right)$
Now simplify it we have,
$ \Rightarrow $360 = $9P$
$ \Rightarrow P = \dfrac{{360}}{9} = 40$ meters.
So the perimeter of a triangular based pyramid is 40 meters.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the formula of lateral surface area of a triangular based pyramid in terms of slant height and perimeter which is stated above, then simply substitute the values in the values in the formula as above and simplify we will get the required perimeter of a triangular based pyramid.