I'll solve each problem step by step, finding the surface area using the nets provided.
Problem 1: Cube with side length 4 cm
The net shows a cube where all sides are 4 cm.
- A cube has 6 faces
- Each face is a square: 4 cm × 4 cm = 16 cm²
- Total surface area = 6 × 16 = 96 cm²
Problem 2: Rectangular prism (5 in × 8 in × 2 in)
Looking at the net, I can identify three different rectangular faces:
- Two faces: 5 in × 8 in = 40 in² each → 2 × 40 = 80 in²
- Two faces: 5 in × 2 in = 10 in² each → 2 × 10 = 20 in²
- Two faces: 8 in × 2 in = 16 in² each → 2 × 16 = 32 in²
Total surface area = 80 + 20 + 32 = 132 in²
Problem 3: Square pyramid
The base is a square: 12 m × 12 m = 144 m²
For the triangular faces:
- Base of triangle = 12 m
- Height of triangle (slant height) = 8 m
- Area of one triangle = ½ × 12 × 8 = 48 m²
- There are 4 triangular faces: 4 × 48 = 192 m²
Total surface area = 144 + 192 = 336 m²
Problem 4: Triangular prism
Two triangular bases:
- Base = 6 ft, Height = 4 ft
- Area of one triangle = ½ × 6 × 4 = 12 ft²
- Two triangles: 2 × 12 = 24 ft²
Three rectangular lateral faces:
- Rectangle 1: 11 ft × 5 ft = 55 ft²
- Rectangle 2: 11 ft × 5 ft = 55 ft²
- Rectangle 3: 11 ft × 6 ft = 66 ft²
Total surface area = 24 + 55 + 55 + 66 = 200 ft²
Final Answer:
1. 96 cm²
2. 132 in²
3. 336 m²
4. 200 ft²
Parent Tip: Review the logic above to help your child master the concept of surface area using nets worksheet.
