Apiece for a board game is shaped like a triangular prism. the piece is 18 millimeters long. the base of the piece is an equilateral triangle with 10 millimeter sides and a height of 9 millimeters. find the surface area of the game piece

So hmmm notice the first picture below
the triangular prism, is really just 2 triangles and 3 rectangles

so... if you get the area of each of the rectangles, and the triangles, add them all up, that's the surface area of the triangular prism

now, notice the second picture, you simply have 3 rectangles, each a 10x18

and notice the triangle, is an equilateral triangle, so all sides are equal, and its altitude or height is given, is 9, so... as you'd know, the area of a triangle is 1/2 bh

so, just get the area of those 3 rectangles and 2 triangles and sum them up, that'd be the area of the triangular prism

Iam unsure about what the proof is, therefore as much as wish to i can not.