Final answer:
To find the surface area of the right triangular prism, calculate the area of the two triangular faces and the three rectangular faces, and sum them up. The total surface area is 120 cm² (option b).
Step-by-step explanation:
To calculate the surface area of a right triangular prism, we need to find the area of all its faces. For this prism, we have two triangular faces and three rectangular faces.
The area of one triangular face is given by the formula for the area of a triangle:
Area = 1/2 × base × height = 1/2 × 5 cm × 12 cm = 30 cm².
This prism has two triangular faces, so the total area for these is:
2 × 30 cm² = 60 cm².
Each of the three rectangular faces has an area equal to the length of one side of the triangular base multiplied by the height of the prism. Therefore, we calculate the areas as follows:
- Rectangle 1 (base × height): 5 cm × 2 cm = 10 cm²
- Rectangle 2 (base × height): 12 cm × 2 cm = 24 cm²
- Rectangle 3 (hypotenuse × height): 13 cm × 2 cm = 26 cm²
Adding the areas of all rectangles together we get:
10 cm² + 24 cm² + 26 cm² = 60 cm².
The total surface area of the prism is the sum of the areas of the triangular faces and the rectangular faces:
60 cm² (triangles) + 60 cm² (rectangles) = 120 cm².
Therefore, the correct option is b. 120.