Let’s solve each problem step by step. We’ll use π = 3.14 as instructed.
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Problem 1: Rectangular Prism (length=8, width=5, height=6)
Surface Area of rectangular prism = 2(lw + lh + wh)
= 2(8×5 + 8×6 + 5×6)
= 2(40 + 48 + 30)
= 2(118) =
236
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Problem 2: Triangular Prism (base triangle: base=6, height=4; prism length=7; sides of triangle: 5, 5, 6)
Surface Area = 2 × area of triangular base + perimeter of base × length
Area of triangle = (1/2) × base × height = (1/2) × 6 × 4 = 12
Perimeter of triangle = 5 + 5 + 6 = 16
Lateral surface area = 16 × 7 = 112
Total SA = 2×12 + 112 = 24 + 112 =
136
*(Note: The diagram shows two equal sides of 5 — so it’s an isosceles triangle with base 6 and legs 5. Height given as 4 checks out via Pythagoras: 3-4-5 right triangle on each side.)*
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Problem 3: Rectangular Prism (length=10, width=4, height=3)
SA = 2(lw + lh + wh)
= 2(10×4 + 10×3 + 4×3)
= 2(40 + 30 + 12)
= 2(82) =
164
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Problem 4: Triangular Prism (right triangle base: legs 3 and 4, hypotenuse 5; prism length=9)
Area of triangle = (1/2) × 3 × 4 = 6
Perimeter = 3 + 4 + 5 = 12
Lateral SA = 12 × 9 = 108
Total SA = 2×6 + 108 = 12 + 108 =
120
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Problem 5: Cube (side = 7)
SA = 6 × s² = 6 × 49 =
294
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Problem 6: Cylinder (radius=5, height=12)
SA = 2πr² + 2πrh
= 2×3.14×25 + 2×3.14×5×12
= 157 + 376.8
=
533.8
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Problem 7: Rectangular Prism (length=6, width=4, height=3)
SA = 2(6×4 + 6×3 + 4×3)
= 2(24 + 18 + 12)
= 2(54) =
108
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Problem 8: Cylinder (diameter=8 → radius=4, height=10)
SA = 2πr² + 2πrh
= 2×3.14×16 + 2×3.14×4×10
= 100.48 + 251.2
=
351.68
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Problem 9: Triangular Prism (triangle base: base=8, height=6; prism length=10; sides: 6, 8, 10? Wait — let’s check.)
Wait — the diagram shows a right triangle? Base 8, height 6 → then hypotenuse = √(8²+6²)=√(64+36)=√100=10. So yes, sides are 6, 8, 10.
Area of triangle = (1/2)×8×6 = 24
Perimeter = 6 + 8 + 10 = 24
Lateral SA = 24 × 10 = 240
Total SA = 2×24 + 240 = 48 + 240 =
288
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Now, compiling all answers in order:
Final Answer:
1. 236
2. 136
3. 164
4. 120
5. 294
6. 533.8
7. 108
8. 351.68
9. 288
Parent Tip: Review the logic above to help your child master the concept of geometry surface area and volume worksheet answers.
