Surface Area of A Triangular Prism | PDF - Free Printable

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

## Problem 1:
Given dimensions:
- Triangle base = 5m, height = 8m
- Prism length = 7m
- Hypotenuse = 9.4m (given)

Step 1: Calculate the two triangular faces
Area of one triangle = ½ × base × height = ½ × 5 × 8 = 20 m²
Two triangles = 20 × 2 = 40 m²

Step 2: Calculate the three rectangular faces
Rectangle 1 (base): 5 × 7 = 35 m²
Rectangle 2 (height side): 8 × 7 = 56 m²
Rectangle 3 (hypotenuse): 9.4 × 7 = 65.8 m²

Step 3: Add all areas
Total = 40 + 35 + 56 + 65.8 = 196.8 m²

## Problem 2:
Given dimensions:
- Triangle base = 6m, height = 12m
- Prism length = 5m
- Hypotenuse = 13.4m (given)

Step 1: Calculate the two triangular faces
Area of one triangle = ½ × 6 × 12 = 36 m²
Two triangles = 36 × 2 = 72 m²

Step 2: Calculate the three rectangular faces
Rectangle 1 (base): 6 × 5 = 30 m²
Rectangle 2 (height side): 12 × 5 = 60 m²
Rectangle 3 (hypotenuse): 13.4 × 5 = 67 m²

Step 3: Add all areas
Total = 72 + 30 + 60 + 67 = 229 m²

## Problem 3:
Given dimensions:
- Triangle base = 12m, height = 10m
- Prism length = 10m
- Hypotenuse = 15.6m (given)

Step 1: Calculate the two triangular faces
Area of one triangle = ½ × 12 × 10 = 60 m²
Two triangles = 60 × 2 = 120 m²

Step 2: Calculate the three rectangular faces
Rectangle 1 (base): 12 × 10 = 120 m²
Rectangle 2 (height side): 10 × 10 = 100 m²
Rectangle 3 (hypotenuse): 15.6 × 10 = 156 m²

Step 3: Add all areas
Total = 120 + 120 + 100 + 156 = 496 m²

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