Calculating Surface Area #2 | Worksheet - Free Printable

I'll solve each surface area problem step by step, carefully checking my calculations.

Problem 1: Cube (top left)
- Dimensions: 5 m × 7 m × 5 m
- This is a rectangular prism with dimensions 5m, 7m, and 5m
- Surface Area = 2(lw + lh + wh)
- SA = 2(5×7 + 5×5 + 7×5)
- SA = 2(35 + 25 + 35)
- SA = 2(95)
- SA = 190 m²

Let me verify: The faces are:
- Two 5×7 faces: 2 × 35 = 70
- Two 5×5 faces: 2 × 25 = 50
- Two 7×5 faces: 2 × 35 = 70
- Total: 70 + 50 + 70 = 190 m² ✓

Problem 2: Cube (top right)
- Dimensions: 8 yd × 8 yd × 8 yd (it's a cube)
- Surface Area of cube = 6s² where s is the side length
- SA = 6 × 8²
- SA = 6 × 64
- SA = 384 yd²

Verification: Each face is 8×8 = 64, and there are 6 faces
6 × 64 = 384 yd² ✓

Problem 3: Triangular Prism (middle left)
- Base triangle: base = 8 in, height = 6 in, sides = 10 in each
- Prism length = 10 in
- Need to find surface area = 2(triangular bases) + 3(rectangular faces)

Area of one triangular base = ½ × base × height = ½ × 8 × 6 = 24 in²
Two triangular bases = 2 × 24 = 48 in²

Rectangular faces:
- Bottom rectangle: 8 × 10 = 80 in²
- Two side rectangles: 10 × 10 = 100 in² each, so 2 × 100 = 200 in²

Total SA = 48 + 80 + 200 = 328 in²

Let me double-check: The triangular base has sides 10, 10, and 8. The three rectangular faces correspond to these three sides, each with length 10.
- Rectangle 1: 8 × 10 = 80
- Rectangle 2: 10 × 10 = 100
- Rectangle 3: 10 × 10 = 100
- Two triangles: 2 × 24 = 48
- Total: 80 + 100 + 100 + 48 = 328 in² ✓

Problem 4: Rectangular Prism (middle right)
- Dimensions: 5 ft × 8.5 ft × 4 ft
- Surface Area = 2(lw + lh + wh)
- SA = 2(5×8.5 + 5×4 + 8.5×4)
- SA = 2(42.5 + 20 + 34)
- SA = 2(96.5)
- SA = 193 ft²

Verification:
- Two 5×8.5 faces: 2 × 42.5 = 85
- Two 5×4 faces: 2 × 20 = 40
- Two 8.5×4 faces: 2 × 34 = 68
- Total: 85 + 40 + 68 = 193 ft² ✓

Problem 5: Triangular Prism (bottom left)
- Base triangle: base = 2.4 mm, height = 1 mm, sides = 1.5 mm and 1.3 mm
- Prism length = 1 mm

Area of triangular base = ½ × 2.4 × 1 = 1.2 mm²
Two triangular bases = 2 × 1.2 = 2.4 mm²

Rectangular faces (corresponding to the three sides of the triangle):
- Rectangle 1: 2.4 × 1 = 2.4 mm²
- Rectangle 2: 1.5 × 1 = 1.5 mm²
- Rectangle 3: 1.3 × 1 = 1.3 mm²

Total SA = 2.4 + 2.4 + 1.5 + 1.3 = 7.6 mm²

Let me verify: 2.4 + 2.4 = 4.8; 4.8 + 1.5 = 6.3; 6.3 + 1.3 = 7.6 mm² ✓

Problem 6: Cube (bottom right)
- Dimensions: 3.1 cm × 3.1 cm × 3.1 cm (it's a cube)
- Surface Area = 6s²
- SA = 6 × 3.1²
- SA = 6 × 9.61
- SA = 57.66 cm²

Verification: 3.1 × 3.1 = 9.61; 6 × 9.61 = 57.66 cm² ✓

Final Answer:
1. 190 m²
2. 384 yd²
3. 328 in²
4. 193 ft²
5. 7.6 mm²
6. 57.66 cm²