Let’s solve each problem step by step.
We are finding the
surface area of rectangular prisms.
A rectangular prism has 6 faces: front/back, left/right, top/bottom.
Opposite faces are equal in size.
The formula for surface area is:
>
Surface Area = 2 × (length × width + length × height + width × height)
Or you can think of it as:
- Find area of front face → multiply by 2 (because back is same)
- Find area of side face → multiply by 2 (because other side is same)
- Find area of top face → multiply by 2 (because bottom is same)
- Add them all up.
Let’s go one by one.
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Problem 1: Dimensions: 3 ft, 5 ft, 7 ft
(We’ll assume: length=5, width=3, height=7 — order doesn’t matter as long as we use all three)
SA = 2 × (5×3 + 5×7 + 3×7)
= 2 × (15 + 35 + 21)
= 2 × 71
=
142 sq ft
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Problem 2: Dimensions: 8 m, 4 m, 3 m
SA = 2 × (8×4 + 8×3 + 4×3)
= 2 × (32 + 24 + 12)
= 2 × 68
=
136 sq m
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Problem 3: Dimensions: 10 in, 9 in, 6 in
SA = 2 × (10×9 + 10×6 + 9×6)
= 2 × (90 + 60 + 54)
= 2 × 204
=
408 sq in
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Problem 4: Dimensions: 12 cm, 5 cm, 7 cm
SA = 2 × (12×5 + 12×7 + 5×7)
= 2 × (60 + 84 + 35)
= 2 × 179
=
358 sq cm
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Problem 5: Dimensions: 9 mm, 3 mm, 14 mm
SA = 2 × (9×3 + 9×14 + 3×14)
= 2 × (27 + 126 + 42)
= 2 × 195
=
390 sq mm
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Problem 6: Dimensions: 15 yd, 7 yd, 9 yd
SA = 2 × (15×7 + 15×9 + 7×9)
= 2 × (105 + 135 + 63)
= 2 × 303
=
606 sq yd
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Problem 7: Dimensions: 11 km, 4 km, 16 km
SA = 2 × (11×4 + 11×16 + 4×16)
= 2 × (44 + 176 + 64)
= 2 × 284
=
568 sq km
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Problem 8: Dimensions: 13 mi, 8 mi, 5 mi
SA = 2 × (13×8 + 13×5 + 8×5)
= 2 × (104 + 65 + 40)
= 2 × 209
=
418 sq mi
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Problem 9: Dimensions: 18 ft, 6 ft, 10 ft
SA = 2 × (18×6 + 18×10 + 6×10)
= 2 × (108 + 180 + 60)
= 2 × 348
=
696 sq ft
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Final Answer:
1. 142 sq ft
2. 136 sq m
3. 408 sq in
4. 358 sq cm
5. 390 sq mm
6. 606 sq yd
7. 568 sq km
8. 418 sq mi
9. 696 sq ft
Parent Tip: Review the logic above to help your child master the concept of volume and surface area of rectangular prism worksheet.
