Surface area worksheet for prisms and cylinders with diagrams and calculation spaces.

I'll help you solve these surface area problems for prisms and cylinders. Let me work through each one step by step.

First, let me identify what I need to calculate:
- Surface area of rectangular prisms (cubes/boxes)
- Surface area of triangular prisms
- Surface area of cylinders

The formulas I'll use:
- Rectangular prism: SA = 2(lw + lh + wh) where l=length, w=width, h=height
- Triangular prism: SA = 2(area of triangle base) + (perimeter of triangle × height of prism)
- Cylinder: SA = 2πr² + 2πrh (or 2πr(r + h))

Let me solve each problem:

Problem A: Rectangular prism with dimensions 10 cm × 5 cm × 8 cm
SA = 2(10×5 + 10×8 + 5×8)
SA = 2(50 + 80 + 40)
SA = 2(170)
SA = 340 cm²

Problem B: Triangular prism with base triangle (base=6 cm, height=4 cm) and prism length=9 cm
Area of triangle = (1/2) × 6 × 4 = 12 cm²
Perimeter of triangle = 6 + 5 + 5 = 16 cm (assuming it's isosceles with sides 5, 5, 6)
SA = 2(12) + 16×9
SA = 24 + 144
SA = 168 cm²

Problem C: Rectangular prism with dimensions 12 cm × 4 cm × 7 cm
SA = 2(12×4 + 12×7 + 4×7)
SA = 2(48 + 84 + 28)
SA = 2(160)
SA = 320 cm²

Problem D: Triangular prism with base triangle (base=8 cm, height=3 cm) and prism length=10 cm
Area of triangle = (1/2) × 8 × 3 = 12 cm²
Perimeter of triangle = 8 + 5 + 5 = 18 cm (assuming isosceles)
SA = 2(12) + 18×10
SA = 24 + 180
SA = 204 cm²

Problem E: Cube with side 9 cm
SA = 6 × s² = 6 × 9² = 6 × 81 = 486 cm²

Problem F: Cylinder with radius 5 cm and height 12 cm
SA = 2πr² + 2πrh = 2πr(r + h)
SA = 2π(5)(5 + 12) = 2π(5)(17) = 170π
Using π ≈ 3.14: SA = 170 × 3.14 = 533.8 cm²

Problem G: Rectangular prism with dimensions 15 cm × 6 cm × 4 cm
SA = 2(15×6 + 15×4 + 6×4)
SA = 2(90 + 60 + 24)
SA = 2(174)
SA = 348 cm²

Problem H: Cylinder with radius 4 cm and height 10 cm
SA = 2πr(r + h)
SA = 2π(4)(4 + 10) = 2π(4)(14) = 112π
Using π ≈ 3.14: SA = 112 × 3.14 = 351.68 cm²

Problem I: Triangular prism with base triangle (base=7 cm, height=5 cm) and prism length=11 cm
Area of triangle = (1/2) × 7 × 5 = 17.5 cm²
Perimeter of triangle = 7 + 6 + 6 = 19 cm (assuming isosceles)
SA = 2(17.5) + 19×11
SA = 35 + 209
SA = 244 cm²

Final Answer:
A: 340 cm²
B: 168 cm²
C: 320 cm²
D: 204 cm²
E: 486 cm²
F: 533.8 cm² (or 170π cm²)
G: 348 cm²
H: 351.68 cm² (or 112π cm²)
I: 244 cm²