Answer:
The surface area of the triangular prism is 180 square centimeters.
Explanation:
To find the surface area of a triangular prism, we need to find the area of each face and add them up. Let's call the base of the triangle b, the height of the triangle h, and the height of the prism (the distance between the two triangular faces) H.
The triangular faces each have an area of (1/2)bh, so the total area of the two triangular faces is bh. The rectangular faces each have an area of Hb, so the total area of the two rectangular faces is 2Hb. Finally, the top and bottom faces each have an area of b^2, so the total area of these two faces is 2b^2.
Adding all of these areas together, we get:
Surface area = bh + 2Hb + 2b^2
Substituting the given values, we get:
Surface area = (6 cm)(8 cm) + 2(5 cm)(6 cm) + 2(6 cm)^2
Surface area = 48 cm^2 + 60 cm^2 + 72 cm^2
Surface area = 180 cm^2
Therefore, the surface area of the triangular prism is 180 square centimeters.