Question

A regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. It has a lateral surface area of 81 square feet. What is the surface area of the regular triangular pyramid?

Answer 1

We know that

[lateral surface area of a regular triangular pyramid]=3*[area of one equilateral triangle]
so
[area of one equilateral triangle]=lateral surface/3-----> 81/3-----> 27 ft²

[surface area of the regular triangular pyramid]=lateral area+area of the base

area of the base is equals to the area of the lateral sides because are equilateral triangles

therefore
area of the base=27 ft²

[surface area of the regular triangular pyramid]=81+27----> 108 ft²

the answer is
the surface area of the regular triangular pyramid is 108 ft²