Final answer:
To find the surface area of a triangular prism, you need to add the areas of all the surfaces. Use the formula for the area of the triangular bases and the formula for the lateral area of a prism. Then, add the areas to get the total surface area.
Step-by-step explanation:
To find the surface area of a triangular prism, you need to add the areas of all the surfaces.
A triangular prism has two triangular bases and three rectangular lateral faces.
The formula for the lateral area of a prism is perimeter of the base times the height. So, to find the surface area:
Find the area of the triangular bases by using the formula (1/2) * base * height.
Find the area of the lateral faces by multiplying the perimeter of each rectangular face by the height.
Add the areas of the bases and the lateral faces to get the total surface area.
So, in this case, the surface area of the triangular prism would be as follows:
Area of triangular bases: (1/2) * 3 * 5 + (1/2) * 11 * 4 = 7.5 + 22 = 29.5 cm²
Area of the rectangular lateral faces: 3 * 11 + 5 * 11 + 4 * 11 = 33 + 55 + 44 = 132 cm²
Total surface area: 29.5 + 132 = 161.5 cm²