Calculate the surface area of triangular prisms with given dimensions.

I'll solve each triangular prism surface area problem step by step.

## Problem 1:
Given: Right triangle base with sides 5m, 8m, and hypotenuse 9.4m; prism length = 7m

Step 1: Calculate the area of the two triangular bases
- Area of one triangle = (1/2) × base × height = (1/2) × 5 × 8 = 20 m²
- Area of both triangles = 2 × 20 = 40 m²

Step 2: Calculate the area of the three rectangular faces
- Rectangle 1: 5m × 7m = 35 m²
- Rectangle 2: 8m × 7m = 56 m²
- Rectangle 3: 9.4m × 7m = 65.8 m²
- Total lateral area = 35 + 56 + 65.8 = 156.8 m²

Step 3: Total Surface Area = 40 + 156.8 = 196.8 m²

## Problem 2:
Given: Right triangle base with sides 6m, 12m, and hypotenuse 13.4m; prism length = 5m

Step 1: Calculate the area of the two triangular bases
- Area of one triangle = (1/2) × 6 × 12 = 36 m²
- Area of both triangles = 2 × 36 = 72 m²

Step 2: Calculate the area of the three rectangular faces
- Rectangle 1: 6m × 5m = 30 m²
- Rectangle 2: 12m × 5m = 60 m²
- Rectangle 3: 13.4m × 5m = 67 m²
- Total lateral area = 30 + 60 + 67 = 157 m²

Step 3: Total Surface Area = 72 + 157 = 229 m²

## Problem 3:
Given: Triangle base with sides 10m, 12m, and third side 15.6m; prism length = 10m

Step 1: Check if this is a right triangle
- 10² + 12² = 100 + 144 = 244
- 15.6² = 243.36 ≈ 244 ✓ (approximately a right triangle)

Step 2: Calculate the area of the two triangular bases
- Area of one triangle = (1/2) × 10 × 12 = 60 m²
- Area of both triangles = 2 × 60 = 120 m²

Step 3: Calculate the area of the three rectangular faces
- Rectangle 1: 10m × 10m = 100 m²
- Rectangle 2: 12m × 10m = 120 m²
- Rectangle 3: 15.6m × 10m = 156 m²
- Total lateral area = 100 + 120 + 156 = 376 m²

Step 4: Total Surface Area = 120 + 376 = 496 m²

Final Answer:
1) 196.8 m²
2) 229 m²
3) 496 m²