To find the total surface area of the triangular prism in problem 1), we need to add up the areas of all its faces.
The prism has:
- Two triangular bases (front and back)
- Three rectangular sides (top, bottom, and side)
From the diagram:
- The triangle has base = 5m, height = 8m
- The length of the prism (distance between the two triangles) = 7m
- The three rectangles have dimensions:
- One: 8m × 7m
- One: 5m × 7m
- One: 9.4m × 7m (this is the slanted side)
Step 1: Area of one triangle
Area = (base × height) ÷ 2
= (5 × 8) ÷ 2
= 40 ÷ 2
= 20 m²
Since there are two identical triangles:
Total triangle area = 20 × 2 = 40 m²
Step 2: Area of the three rectangles
Rectangle 1: 8m × 7m = 56 m²
Rectangle 2: 5m × 7m = 35 m²
Rectangle 3: 9.4m × 7m = 65.8 m²
Add them: 56 + 35 + 65.8 = 156.8 m²
Step 3: Total surface area
Add triangle areas and rectangle areas:
40 + 156.8 = 196.8 m²
Final Answer:
196.8
Parent Tip: Review the logic above to help your child master the concept of surface area and volume of triangular prisms worksheet.
