Surface Area of a Rectangular Prism - Practice Problems

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: add up the areas of all 6 faces.

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Problem 1: Dimensions 5m × 7m × 4m

Faces:
- Front & Back: 5 × 4 = 20 → two of them → 40
- Left & Right: 7 × 4 = 28 → two of them → 56
- Top & Bottom: 5 × 7 = 35 → two of them → 70

Total = 40 + 56 + 70 = 166 m²

Check with formula:
2×(5×7 + 5×4 + 7×4) = 2×(35 + 20 + 28) = 2×83 = 166 m² ✔

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Problem 2: Dimensions 10cm × 3cm × 5cm

Wait — looking at diagram: it says 10 cm tall, 3 cm wide, and depth? The label “5 cm” is on the side edge — so likely dimensions are:
Height = 10 cm, Width = 3 cm, Depth = 5 cm

So: length=5, width=3, height=10

Surface Area = 2×(5×3 + 5×10 + 3×10) = 2×(15 + 50 + 30) = 2×95 = 190 cm²

Check manually:
- Front/Back: 5×10 = 50 → 100
- Left/Right: 3×10 = 30 → 60
- Top/Bottom: 5×3 = 15 → 30
Total = 100+60+30 = 190 cm² ✔

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Problem 3: Dimensions 9in × 2in × 3in

Labeling: 9 in long, 2 in high, 3 in deep? Diagram shows 9 in along base, 2 in vertical, 3 in going back.

So: l=9, w=3, h=2

SA = 2×(9×3 + 9×2 + 3×2) = 2×(27 + 18 + 6) = 2×51 = 102 in²

Manual check:
- Front/Back: 9×2 = 18 → 36
- Left/Right: 3×2 = 6 → 12
- Top/Bottom: 9×3 = 27 → 54
Total = 36+12+54 = 102 in² ✔

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Problem 4: Dimensions 5ft × 3ft × 6ft

Diagram: 5 ft front width, 3 ft depth, 6 ft height? Wait — labels say: 5 ft (front), 3 ft (side depth), 6 ft (height). So l=5, w=3, h=6

SA = 2×(5×3 + 5×6 + 3×6) = 2×(15 + 30 + 18) = 2×63 = 126 ft²

Manual:
- Front/Back: 5×6 = 30 → 60
- Left/Right: 3×6 = 18 → 36
- Top/Bottom: 5×3 = 15 → 30
Total = 60+36+30 = 126 ft² ✔

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Problem 5: Dimensions 4m × 2m × 6m

Labels: 4 m (width), 2 m (depth), 6 m (height)

So l=4, w=2, h=6

SA = 2×(4×2 + 4×6 + 2×6) = 2×(8 + 24 + 12) = 2×44 = 88 m²

Manual:
- Front/Back: 4×6 = 24 → 48
- Left/Right: 2×6 = 12 → 24
- Top/Bottom: 4×2 = 8 → 16
Total = 48+24+16 = 88 m² ✔

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Problem 6: Dimensions 5ft × 4ft × 3ft

Labels: 5 ft (length), 4 ft (width), 3 ft (height)? Diagram shows 5 ft front, 4 ft side, 3 ft height.

Actually, let’s read carefully: it says 5 ft (along bottom front), 4 ft (going back), 3 ft (up). So l=5, w=4, h=3

SA = 2×(5×4 + 5×3 + 4×3) = 2×(20 + 15 + 12) = 2×47 = 94 ft²

Manual:
- Front/Back: 5×3 = 15 → 30
- Left/Right: 4×3 = 12 → 24
- Top/Bottom: 5×4 = 20 → 40
Total = 30+24+40 = 94 ft² ✔

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Problem 7: Dimensions 4m × 4m × 6m

It’s a square base: 4m x 4m, height 6m

SA = 2×(4×4 + 4×6 + 4×6) = 2×(16 + 24 + 24) = 2×64 = 128 m²

Manual:
- Front/Back: 4×6 = 24 → 48
- Left/Right: 4×6 = 24 → 48
- Top/Bottom: 4×4 = 16 → 32
Total = 48+48+32 = 128 m² ✔

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Problem 8: Dimensions 6cm × 6cm × 4cm

Square base again: 6x6, height 4

SA = 2×(6×6 + 6×4 + 6×4) = 2×(36 + 24 + 24) = 2×84 = 168 cm²

Manual:
- Front/Back: 6×4 = 24 → 48
- Left/Right: 6×4 = 24 → 48
- Top/Bottom: 6×6 = 36 → 72
Total = 48+48+72 = 168 cm² ✔

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Problem 9: Dimensions 3ft × 4ft × 5ft

Labels: 3 ft (width), 4 ft (depth), 5 ft (height)

So l=3, w=4, h=5

SA = 2×(3×4 + 3×5 + 4×5) = 2×(12 + 15 + 20) = 2×47 = 94 ft²

Manual:
- Front/Back: 3×5 = 15 → 30
- Left/Right: 4×5 = 20 → 40
- Top/Bottom: 3×4 = 12 → 24
Total = 30+40+24 = 94 ft² ✔

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Final Answer:

1. 166 m²
2. 190 cm²
3. 102 in²
4. 126 ft²
5. 88 m²
6. 94 ft²
7. 128 m²
8. 168 cm²
9. 94 ft²