Math worksheet with geometry problems on perimeter and area.

It looks like you've uploaded a photo of a math worksheet that involves calculating the perimeter and area of various rectangles and squares. The student has already worked on several problems, but some are incomplete or need verification.

Let’s go through the problems systematically and solve them step by step. I’ll explain how to find both perimeter and area for each shape.

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🔷 Key Formulas:

- Perimeter of a rectangle = 2 × (length + width)
- Area of a rectangle = length × width
- For squares, all sides are equal:
- Perimeter = 4 × side
- Area = side²

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Let’s analyze the visible problems:

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✔ Problem (1): Rectangle with dimensions 4 cm and 8 cm

- Given: Length = 8 cm, Width = 4 cm
- Perimeter = 2 × (8 + 4) = 2 × 12 = 24 cm
- Area = 8 × 4 = 32 cm²

✔ Student wrote:
- Perimeter: 24 cm → ✔️ Correct
- Area: 32 cm² → ✔️ Correct

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✔ Problem (2): Rectangle with dimensions 7 cm and 4 cm

- Given: 7 cm and 4 cm
- Perimeter = 2 × (7 + 4) = 2 × 11 = 22 cm
- Area = 7 × 4 = 28 cm²

But student wrote:
- Perimeter: 20 cm ✘ Incorrect
- Area: 18 cm² ✘ Incorrect

👉 Correction:
- Perimeter: 22 cm
- Area: 28 cm²

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✔ Problem (3): Rectangle with dimensions 3 cm and 2 cm

- Perimeter = 2 × (3 + 2) = 2 × 5 = 10 cm
- Area = 3 × 2 = 6 cm²

✔ Student wrote:
- Perimeter: 10 cm → ✔️
- Area: 6 cm² → ✔️

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✔ Problem (4): Rectangle with dimensions 7 cm and 5 cm

- Perimeter = 2 × (7 + 5) = 2 × 12 = 24 cm
- Area = 7 × 5 = 35 cm²

Student wrote:
- Perimeter: 27 cm ✘ Incorrect
- Area: 52 cm² ✘ Incorrect

Wait — they wrote:
- (A) 7×4=28 cm² → this is wrong because it's not 4, it's 5.
- (B) 5×5=25 cm² → this is a square, not the given rectangle.

The figure shows a rectangle with 7 cm and 5 cm, so:
- Correct area = 7 × 5 = 35 cm²
- Correct perimeter = 2 × (7 + 5) = 24 cm

So student made an error here.

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✔ Problem (5): Square with side 4 m

- Perimeter = 4 × 4 = 16 m
- Area = 4 × 4 = 16 m²

Student wrote:
- Perimeter: 16 m → ✔️
- Area: 16 m² → ✔️

Wait — student wrote 18 m²? That’s incorrect.

✘ Student wrote: Area = 18 m² → ✘ Wrong

✔ Correct: 16 m²

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✔ Problem (6): Rectangle with 4 m and 3 m

- Perimeter = 2 × (4 + 3) = 2 × 7 = 14 m
- Area = 4 × 3 = 12 m²

Student wrote:
- Perimeter: 14 m → ✔️
- Area: 12 m² → ✔️

✔ Correct!

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✔ Problem (7): Rectangle with 4 m and 5 m

- Perimeter = 2 × (4 + 5) = 2 × 9 = 18 m
- Area = 4 × 5 = 20 m²

Student wrote:
- Perimeter: 18 m → ✔️
- Area: 20 m² → ✔️

✔ Correct!

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✔ Problem (8): Rectangle with 3 cm and 2 cm

- Perimeter = 2 × (3 + 2) = 2 × 5 = 10 cm
- Area = 3 × 2 = 6 cm²

Student left blank → needs to fill in:
- Perimeter: 10 cm
- Area: 6 cm²

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✔ Problem (9): Rectangle with 3 cm and 3 cm (a square)

- Perimeter = 4 × 3 = 12 cm
- Area = 3 × 3 = 9 cm²

Student left blank → should write:
- Perimeter: 12 cm
- Area: 9 cm²

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Summary of Corrections:

| Problem | Perimeter | Area | Student Answer | Correct? |
|--------|-----------|------|----------------|---------|
| (1) | 24 cm | 32 cm² | 24 cm, 32 cm² | ✔️ |
| (2) | 22 cm | 28 cm² | 20 cm, 18 cm² | ✘ |
| (3) | 10 cm | 6 cm² | 10 cm, 6 cm² | ✔️ |
| (4) | 24 cm | 35 cm² | 27 cm, 52 cm² | ✘ |
| (5) | 16 m | 16 m² | 16 m, 18 m² | ✘ (Area wrong) |
| (6) | 14 m | 12 m² | 14 m, 12 m² | ✔️ |
| (7) | 18 m | 20 m² | 18 m, 20 m² | ✔️ |
| (8) | 10 cm | 6 cm² | Blank | ✘ (needs filling) |
| (9) | 12 cm | 9 cm² | Blank | ✘ (needs filling) |

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Final Notes:

- The student seems to have mixed up dimensions in some cases (e.g., used 4 instead of 5).
- Also, in problem (5), they incorrectly calculated area as 18 m² instead of 16 m².
- Some problems were left blank.

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✔ Suggested Fixes:

1. Problem (2):
- Perimeter: 22 cm
- Area: 28 cm²

2. Problem (4):
- Perimeter: 24 cm
- Area: 35 cm²

3. Problem (5):
- Area should be 16 m², not 18 m²

4. Problem (8):
- Perimeter: 10 cm
- Area: 6 cm²

5. Problem (9):
- Perimeter: 12 cm
- Area: 9 cm²

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Let me know if you'd like a clean version of the corrected worksheet!