Let’s solve each rectangular prism one by one.
The formula for surface area of a rectangular prism is:
Surface Area = 2 × (length × width + length × height + width × height)
We’ll plug in the numbers for each shape and calculate carefully.
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First Prism:
Dimensions: 12 in (length), 2 in (width), 3 in (height)
→ SA = 2 × (12×2 + 12×3 + 2×3)
= 2 × (24 + 36 + 6)
= 2 × 66
=
132 square inches
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Second Prism:
Dimensions: 8 m (length), 6 m (width), 22 m (height)
→ SA = 2 × (8×6 + 8×22 + 6×22)
= 2 × (48 + 176 + 132)
= 2 × 356
=
712 square meters
Wait — let me double-check that addition:
48 + 176 = 224; 224 + 132 = 356 → yes, correct.
2 × 356 = 712 → correct.
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Third Prism:
Dimensions: 29 ft (length), 16 ft (width), 23 ft (height)
→ SA = 2 × (29×16 + 29×23 + 16×23)
Calculate each part:
- 29 × 16 = 464
- 29 × 23 = let’s do 30×23 = 690 minus 1×23 = 23 → 690 - 23 = 667
- 16 × 23 = 16×20 + 16×3 = 320 + 48 = 368
Now add them: 464 + 667 + 368
→ 464 + 667 = 1131; 1131 + 368 = 1499
Then multiply by 2: 2 × 1499 =
2998 square feet
Double-check:
464 + 667 = 1131 ✔️
1131 + 368: 1131 + 300 = 1431; 1431 + 68 = 1499 ✔️
2 × 1499 = 2998 ✔️
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Fourth Prism:
Dimensions: 4 cm (length), 1.2 cm (width), 2.8 cm (height)
→ SA = 2 × (4×1.2 + 4×2.8 + 1.2×2.8)
Calculate each:
- 4 × 1.2 = 4.8
- 4 × 2.8 = 11.2
- 1.2 × 2.8 → Let’s compute: 1.2 × 2 = 2.4; 1.2 × 0.8 = 0.96 → total = 2.4 + 0.96 = 3.36
Add them: 4.8 + 11.2 + 3.36
→ 4.8 + 11.2 = 16.0; 16.0 + 3.36 = 19.36
Multiply by 2: 2 × 19.36 =
38.72 square centimeters
Check:
4.8 + 11.2 = 16 ✔️
16 + 3.36 = 19.36 ✔️
2 × 19.36 = 38.72 ✔️
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Final Answer:
132 in², 712 m², 2998 ft², 38.72 cm²
Parent Tip: Review the logic above to help your child master the concept of surface area of rectangular prism worksheet.
