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?
Accepted Solution
A:
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