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 three different faces (since opposite ones are same)
- Add them up
- Multiply by 2
Let’s go one by one.
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Problem 1: Dimensions: 3 cm, 4 cm, 5 cm
(Assume: length=5, width=3, height=4 — order doesn’t matter as long as we use all three)
Area of faces:
- 5×3 = 15
- 5×4 = 20
- 3×4 = 12
Sum = 15+20+12 = 47
Multiply by 2 → 94 cm²
✔ Check: 2*(15+20+12) = 2*47 = 94 ✔️
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Problem 2: Dimensions: 8 in, 5 in, 4 in
Faces:
- 8×5 = 40
- 8×4 = 32
- 5×4 = 20
Sum = 40+32+20 = 92
×2 = 184 in²
✔ Check: 2*(40+32+20)=2*92=184 ✔️
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Problem 3: Dimensions: 6 ft, 6 ft, 6 ft → This is a cube!
All faces same: 6×6 = 36
6 faces → 6×36 = 216 ft²
OR using formula: 2*(6×6 + 6×6 + 6×6) = 2*(36+36+36)=2*108=216 ✔️
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Problem 4: Dimensions: 7 m, 5 m, 3 m
Faces:
- 7×5 = 35
- 7×3 = 21
- 5×3 = 15
Sum = 35+21+15 = 71
×2 = 142 m²
✔ Check: 2*(35+21+15)=2*71=142 ✔️
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Problem 5: Dimensions: 5 ft, 3 ft, 7 ft
Same numbers as #4? Wait — let’s check: 5, 3, 7 → same as 7,5,3 → so same answer!
Faces:
- 5×3 = 15
- 5×7 = 35
- 3×7 = 21
Sum = 15+35+21 = 71
×2 = 142 ft²
✔ Same as #4 → 142 ✔️
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Problem 6: Dimensions: 9 yd, 5 yd, 4 yd
Faces:
- 9×5 = 45
- 9×4 = 36
- 5×4 = 20
Sum = 45+36+20 = 101
×2 = 202 yd²
✔ Check: 2*(45+36+20)=2*101=202 ✔️
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Problem 7: Dimensions: 10 cm, 4 cm, 6 cm
Faces:
- 10×4 = 40
- 10×6 = 60
- 4×6 = 24
Sum = 40+60+24 = 124
×2 = 248 cm²
✔ Check: 2*(40+60+24)=2*124=248 ✔️
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Problem 8: Dimensions: 12 m, 5 m, 4 m
Faces:
- 12×5 = 60
- 12×4 = 48
- 5×4 = 20
Sum = 60+48+20 = 128
×2 = 256 m²
✔ Check: 2*(60+48+20)=2*128=256 ✔️
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Problem 9: Dimensions: 8 in, 5 in, 4 in → Same as Problem 2!
So again: 2*(8×5 + 8×4 + 5×4) = 2*(40+32+20)=2*92=184 in²
✔ Confirmed: 184 ✔️
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Final Answer:
1. 94 cm²
2. 184 in²
3. 216 ft²
4. 142 m²
5. 142 ft²
6. 202 yd²
7. 248 cm²
8. 256 m²
9. 184 in²
Parent Tip: Review the logic above to help your child master the concept of volume and surface area of rectangular prisms worksheet.
