The base of a triangular prism is an equilateral triangle with a perimeter of 15in. if the height of the prism is 4in, find the surface area.

We know that
surface area=2*[area of the base]+perimeter of the base*height 
find the area of the base

is an equilateral triangle
b=15/3> 5 in
applying the law of sines to find the area
Area=(1/2)*b²*sin 60°> area=(1/2)*5²*sin 60°> 10.8253 in²

alternative method to find the area of the equilateral triangle
find the h value
applying the Pythagoras theorem
h²=5²-2.5²> h=√18.75> h=4.33 in
area=b*h/2> area=5*4.33/2> 10.8253 in²

surface area=2*[10.8253]+15*4>  81.65 in²

the answer is
81.65 in²