Surface Area - Digital and Printable - Free Printable

Let's go through each problem on the worksheet and verify the surface area calculations, explaining the reasoning step by step.

---

Problem 1: Cube with side length 3 cm

- All sides are equal (cube).
- Area of one face = $ 3 \times 3 = 9 \, \text{cm}^2 $
- There are 6 faces → Total Surface Area = $ 6 \times 9 = 54 \, \text{cm}^2 $

✔ Correct.

---

Problem 2: Cube with side length 4 cm

- Area of one face = $ 4 \times 4 = 16 \, \text{cm}^2 $
- Total Surface Area = $ 6 \times 16 = 96 \, \text{cm}^2 $

✔ Correct.

---

Problem 3: Rectangular Prism (2 ft × 2 ft × 6 ft)

Dimensions:
- Length = 6 ft
- Width = 2 ft
- Height = 2 ft

Faces:
- Two faces: $ 6 \times 2 = 12 \, \text{ft}^2 $ → Side 1 & 2
- Two faces: $ 6 \times 2 = 12 \, \text{ft}^2 $ → Side 3 & 4
- Two faces: $ 2 \times 2 = 4 \, \text{ft}^2 $ → Side 5 & 6

Total Surface Area:
$$
2(12) + 2(12) + 2(4) = 24 + 24 + 8 = 56 \, \text{ft}^2
$$

But the answer is written as 56 cm², which is incorrect due to unit mismatch.

⚠️ Error: The dimensions are in feet, so the area should be in square feet, not square centimeters.

✔ Corrected: 56 ft²

---

Problem 4: Rectangular Prism (5 m × 3 m × 10 m)

Dimensions:
- Length = 10 m
- Width = 5 m
- Height = 3 m

Face areas:
- Front/Back: $ 10 \times 3 = 30 \, \text{m}^2 $
- Left/Right: $ 5 \times 3 = 15 \, \text{m}^2 $
- Top/Bottom: $ 10 \times 5 = 50 \, \text{m}^2 $

So:
- Side 1 & 2: 50 cm² ✘ → Should be 50 m²
- Side 3 & 4: 30 cm² ✘ → Should be 30 m²
- Side 5 & 6: 15 cm² ✘ → Should be 15 m²

Total Surface Area:
$$
2(50) + 2(30) + 2(15) = 100 + 60 + 30 = 190 \, \text{m}^2
$$

But the answer is given as 190 cm² — again, unit error.

⚠️ Error: Units should be m², not cm².

✔ Corrected: 190 m²

---

Problem 5: Square Pyramid

Base: 8 ft × 8 ft
Triangular faces: 4 congruent triangles
Height of triangle (slant height): 10 ft

Wait — the base is labeled 8 ft, but the side of the triangular face is labeled 5 ft? That doesn’t match.

Looking closely:

- Base: 8 ft
- Slant height (height of triangle): 10 ft
- But it says "5 ft" on the edge of the triangle?

Actually, the diagram shows:
- Base = 8 ft
- One triangular face has a base of 8 ft and a height of 10 ft (from apex to base)
- But then it labels a side as 5 ft — possibly a mistake?

Wait — the label “5 ft” appears next to the triangular face, but that may be a typo or mislabeling.

Assuming:
- Base of pyramid: 8 ft × 8 ft
- Each triangular face has base = 8 ft, height = 10 ft

Then:
- Area of one triangular face = $ \frac{1}{2} \times 8 \times 10 = 40 \, \text{ft}^2 $
- Four triangular faces: $ 4 \times 40 = 160 \, \text{ft}^2 $
- Base area = $ 8 \times 8 = 64 \, \text{ft}^2 $

Total Surface Area = $ 160 + 64 = 224 \, \text{ft}^2 $

But the answer is written as 224 cm², and the units in the calculation are cm² — another unit inconsistency.

Also, the side lengths are in feet, so area should be in square feet.

⚠️ Error: Units are mixed up. It should be 224 ft², not cm².

---

✔ Summary of Corrections:

| Problem | Correct Answer | Unit Error? |
|--------|----------------|-------------|
| 1 | 54 cm² | ✔ Correct |
| 2 | 96 cm² | ✔ Correct |
| 3 | 56 ft² | ✘ Should be ft², not cm² |
| 4 | 190 m² | ✘ Should be m², not cm² |
| 5 | 224 ft² | ✘ Should be ft², not cm² |

---

🔍 Final Notes:

- Problem 3: Dimensions are in feet, so area must be in ft².
- Problem 4: Dimensions are in meters, so area must be in m².
- Problem 5: Dimensions are in feet, so area must be in ft².
- All answers were calculated correctly numerically, but units were incorrectly labeled as cm² in problems 3–5.

---

✔ Final Correct Answers:

1. 54 cm²
2. 96 cm²
3. 56 ft²
4. 190 m²
5. 224 ft²

> 🟩 The numerical values are correct, but the units need to be fixed for problems 3, 4, and 5.