To calculate the surface area of a triangular prism, you need to find the area of each face and then add them together.
1. The area of the front triangle can be found using the formula for the area of a triangle: 1/2 * base * height. Since it is a right triangle, the height can be found using the Pythagorean theorem: a^2 + b^2 = c^2. In this case, a = 6 cm, b = 8 cm, and c (the hypotenuse) = 10 cm. So, the height of the triangle is sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8 cm. The area of the triangle is therefore 1/2 * 6 cm * 8 cm = 24 cm^2.
2. The area of the right rectangle is simply length * width, which is 8 cm * 9 cm = 72 cm^2.
3. Since the prism has two identical triangular faces (front and back) and three identical rectangular faces (top, bottom, and side), we can multiply the area of each face by 2 (for the triangles) or 3 (for the rectangles) to get the total surface area.
So, the total surface area of the triangular prism is 2(24 cm^2) + 3(72 cm^2) = 48 cm^2 + 216 cm^2 = 264 cm^2.