Question

A triangular prism has a Surface Area of 48.735 km2. The base of the prism is a triangle with a height of 3 and an unknown base. The distance between the bases of the prism is 12 km. Find the measure of the base of the triangle.
Choices: 4.8 ;  3.9 ;  2.5 ;  3.46

Answer 1

we assume that the triangle of the base is equilateral, the three sides are equal

we know that

[surface area of the prism]=2*[area of the base]+perimeter of the base*height 
surface area=48.735 km²
height=12 km

area of the base=b*h/2-----> area of the triangle

b is the measure of the base of the triangle
h=3 km
area of the base=3*b/2 km²

perimeter of the triangle=3*b

48.735=2*[3*b/2]+3*b*12-----> 48.735=3*b+36*b----> 48.735=39*b
b=48.735/39-----> b=1.25 km

the answer is
The measure of the base of the triangle is 1.25 km