The surface area of a triangular prism can be calculated by adding the area of the triangular base to the area of the three rectangular lateral faces.
First, we'll find the area of the triangular base. Since the triangle is isosceles and has a right angle, we know that the base is a 19 in. by 19 in. square. The area of this square is 19 in. x 19 in. = 361 in^2
Next, we'll find the area of each lateral face. Since the triangular prism is 42 in. long and the base is 19 in. wide, we know that the height of each lateral face is 42 in. The area of each lateral face is 42 in. x 19 in. = 798 in^2
To find the total surface area of the triangular prism, we add the area of the base to the area of the three lateral faces:
Surface area = 361 in^2 + 3(798 in^2) = 361 in^2 + 2394 in^2 = 2755 in^2
To find the surface area of resulting prism, We just need to find the area of the resulting rectangle after gluing the lateral faces with the 26.9-in. sides together.
Surface area of resulting prism = 42 in x 26.9 in = 1138 in^2
So, the surface area of each triangular prism is 2755 square inches, and the surface area of the resulting prism after gluing the lateral faces with the 26.9-in. sides together is 1138 square inches.