The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.
The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.
So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.
16√3 = (sqrt(3)/4) * s^2
s = (4*16√3)/sqrt(3) = 16√3 cm
Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.
Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²
This simplifies to:
960√3 cm²
So the total area of the rectangular surface of the prism is 960√3 square cm.