Enquiry-Based Maths: Real Life Maths: Measuring the Area and ... - Free Printable

You’ve uploaded a handwritten math worksheet titled “Area + Perimeter”, where the task is to measure the area and perimeter of each room in a house plan drawn on grid paper. The key says:
> 1 cm² = 1 m²

This means each small square on the grid represents 1 square meter, and each side of a square is 1 meter long.

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## ✔ How to Solve This Problem

To find area and perimeter for each room:

➤ Area:

- Count the number of full 1 cm × 1 cm squares inside the room.
- If there are partial squares (like half-squares), you can estimate or combine them to make whole squares.
- Since 1 cm² = 1 m², the count equals the area in m².

➤ Perimeter:

- Trace the outer boundary of the room.
- Count how many 1 cm line segments (edges of squares) form the boundary.
- Each segment = 1 meter → total count = perimeter in meters (m).

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## 📐 Let’s Verify the Given Answers Room by Room

*(Note: I’ll assume the student counted correctly unless there’s a clear error.)*

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1. Living Room

- Area: 24 m² → likely 6 units wide × 4 units tall = 24 ✓
- Perimeter: 20 m → (6+4)×2 = 20 ✓
✔ Correct

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2. Dining Room

- Area: 16 m² → 4×4 = 16 ✓
- Perimeter: 16 m → (4+4)×2 = 16 ✓
✔ Correct

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3. Main Bedroom

- Area: 12 m² → 4×3 = 12 ✓
- Perimeter: 10 m → (4+3)×2 = 14 ✘ — Wait, this doesn’t match!

> ❗ Error here!
If it’s 4m × 3m, perimeter should be 14 m, not 10 m.
But maybe the shape is irregular? Looking at the drawing, if it’s L-shaped or has an indent, perimeter might be less.

Looking at the image: Main bedroom appears rectangular, 4 units wide, 3 units tall → perimeter should be 14 m.

👉 Likely mistake: Student wrote 10 instead of 14.

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4. Second Bedroom

- Area: 11 m² → possibly 3×3 + 2 extra squares? Or irregular shape → plausible.
- Perimeter: 9 m → hard to get 9 with integer sides. For example, 3×3 = 9 area, but perimeter 12.
If it’s 4×2 + 3 extra? Unlikely to get 9m perimeter.

Looking at the drawing — second bedroom seems to be 3 units wide, 4 units tall? That would be 12 area, 14 perimeter.

👉 This one also looks wrong. Area 11 is possible if irregular, but perimeter 9 is very low — maybe miscounted.

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5. Ensuite

- Area: 5 m² → 2×2 + 1 = 5? Or 5 single squares → possible.
- Perimeter: 5 m → unusual. Minimum perimeter for 5 squares is 10–12 depending on arrangement.
Example: 5 in a row → perimeter = 2×(5+1)=12.
Even if compact (like 2x2 + 1 attached), perimeter is ~10–12.

👉 Perimeter 5 m is impossible. Must be a mistake.

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6. Kitchen

- Area: 8 m² → 4×2 = 8 ✓
- Perimeter: 7 m → (4+2)×2 = 12 ✘ — Again, mismatch.

If it’s 4×2 rectangle, perimeter must be 12 m.
Unless it shares walls with other rooms? But perimeter usually counts external boundary only.

In floor plans, sometimes internal walls are not counted — but perimeter should still include all outer edges of the room.

👉 Perimeter should be 12 m, not 7 m.

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7. Hallway

- Area: 7 m² → could be 7 single squares in a line or L-shape → plausible.
- Perimeter: 7 m → again, too low. Even 7 in a row → perimeter = 2×(7+1)=16.

👉 Perimeter 7 m is impossible. Mistake.

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8. Varandah

- Area: 57 m² → large surrounding area — plausible.
- Perimeter: 53 m → since it wraps around, this could be correct if measured properly.

Let’s check: Whole house including varandah has perimeter 50 m — which is smaller than varandah alone? That doesn’t make sense.

Wait — the whole house (including varandah) is listed as:
> A = 150 m², P = 50 m² ✘ — Units error!

Perimeter cannot be in m² — it should be m.

Also, if varandah alone has perimeter 53 m, but the whole house (which includes varandah) has only 50 m? That’s impossible — the whole house perimeter should be less than or equal to varandah’s if varandah surrounds it.

Actually, looking at the drawing — the varandah is the outermost border. So the whole house perimeter should be the same as the varandah’s outer perimeter.

So if varandah P = 53 m, then whole house P should also be 53 m.

But student wrote:
> Whole house: P = 50 m² ← ✘ Wrong unit and value.

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9. Bathroom + Toilet

- Area: 6 m² → 3×2 = 6 ✓
- Perimeter: 6 m → (3+2)×2 = 10 ✘ — Again, mismatch.

Should be 10 m if rectangular.

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10. Laundry

- Area: 4 m² → 2×2 = 4 ✓
- Perimeter: 4 m → (2+2)×2 = 8 ✘ — Should be 8 m.

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## 🔍 Summary of Errors:

| Room | Area Correct? | Perimeter Correct? | Notes |
|----------------|---------------|--------------------|-------|
| Living Room | ✔ Yes | ✔ Yes | |
| Dining Room | ✔ Yes | ✔ Yes | |
| Main Bedroom | ✔ Yes | ✘ No (should be 14) | Wrote 10 |
| Second Bedroom | ⚠️ Maybe | ✘ No | 11 area possible, 9 perimeter impossible |
| Ensuite | ⚠️ Maybe | ✘ No | 5 area possible, 5 perimeter impossible |
| Kitchen | ✔ Yes | ✘ No (should be 12) | Wrote 7 |
| Hallway | ⚠️ Maybe | ✘ No | 7 area possible, 7 perimeter impossible |
| Varandah | ✔ Likely | ⚠️ Questionable | 53 m possible, but whole house perimeter conflict |
| Bathroom | ✔ Yes | ✘ No (should be 10) | Wrote 6 |
| Laundry | ✔ Yes | ✘ No (should be 8) | Wrote 4 |
| Whole House | ✔ 150 m² | ✘ 50 m² (unit error) | Should be 50 m |

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## 🧮 Total Area Check:

Add up all room areas:

- Living: 24
- Dining: 16
- Main Bed: 12
- Second Bed: 11
- Ensuite: 5
- Kitchen: 8
- Hallway: 7
- Varandah: 57
- Bathroom: 6
- Laundry: 4

Total = 24+16=40; +12=52; +11=63; +5=68; +8=76; +7=83; +57=140; +6=146; +4=150 ✔

So total area = 150 m² — matches the “whole house” area. Good!

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## 🛠️ Recommendations for Correction:

1. Fix perimeter calculations using the formula:
> For rectangles: P = 2 × (length + width)
For irregular shapes: count every outer edge segment.

2. Double-check shapes — some rooms may share walls, but perimeter still counts all outer boundaries.

3. Never write perimeter in m² — always m.

4. Varandah perimeter should equal whole house perimeter — since varandah is the outer boundary.

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## ✔ Final Answer (Corrected):

Here’s what the answers *should* be (based on standard grid counting and assuming rectangular shapes where possible):

| Room | Area (m²) | Perimeter (m) |
|----------------|-----------|---------------|
| Living Room | 24 | 20 |
| Dining Room | 16 | 16 |
| Main Bedroom | 12 | 14 |
| Second Bedroom | 11 | ~14–16 |
| Ensuite | 5 | ~10–12 |
| Kitchen | 8 | 12 |
| Hallway | 7 | ~14–16 |
| Varandah | 57 | 53 |
| Bathroom | 6 | 10 |
| Laundry | 4 | 8 |
| Whole House| 150 | 53 |

*(Note: For irregular rooms like hallway, ensuite, second bedroom — actual perimeter depends on exact shape. Use grid counting for accuracy.)*

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## 🎯 Teaching Tip:

When teaching area and perimeter:
- Use grid paper to visualize.
- For area: count squares.
- For perimeter: trace the outline and count edges.
- Always check units: area = m², perimeter = m.
- Rectangles: easy formulas. Irregular shapes: count manually.

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✔ You did a great job counting areas! Just double-check perimeters — they’re trickier. Keep practicing!

Let me know if you want me to redraw the corrected version or explain any specific room’s measurement.