Atriangular 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.

The surface area of the prism is equal to the summed up area of the faces of the triangular prism.

The bases of the prism would be triangles with an unknown base, b, and height of 3. The area of the base is calculated through the equation,
          A = bh/2
where b is base and h is height. Substituting the values,
       A = b(3)/2

Since there are two bases, the contribution of the triangles for the surface area is,
   2A = 3b

Next we calculate for the area of the triangle sides with length equal to b (same as the base of the triangle). 
   Area = b(12 km)
There are 3 sides such that the total area becomes,
   Area = 36b

Hence, the surface area is,
    48.735 km² = 3b + (36b)

The value of b from the equation is 1.25 km

ANSWER: 1.25 km