Triangular prism

To find the area of the triangular base of the prism, we can use the formula for the area of a triangle: 1/2 * base * height. Since the base of the triangle is 7cm and the height is 6cm, the area of the triangular base is:

1/2 * 7cm * 6cm = 21 square centimeters

To find the area of the smallest rectangle of the prism, we can use the formula for the area of a rectangle: length * width. Since the dimensions are 4cm and 6cm, the area of the smallest rectangle is:
4cm * 6cm = 24 square centimeters

To find the area of the largest rectangle of the prism, we can use the dimensions 7cm and 12cm:
7cm * 12cm = 84 square centimeters

The total surface area of the triangular prism is the sum of the areas of the triangular base, the two rectangles on the sides, and the top and bottom rectangles. The total surface area is:
2(base area) + 2(smallest rectangle area) + 2(largest rectangle area) =
2(21) + 2(24) + 2(84) = 42 + 48 + 168 = 258 square centimeters

Therefore, the total surface area of the triangular prism is 258 square centimeters.