House Project - Detailed hand-drawn floor plan showing room layouts, dimensions, and garden space.

It looks like you've uploaded a hand-drawn architectural floor plan for a "House Project," with various rooms, measurements, and calculations. Let's break down the image and solve the problem step by step.

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🔍 Overview of the Image

The drawing is a floor plan of a house, showing:

- Dimensions (in meters)
- Room labels (e.g., kitchen, living room, bedrooms)
- Calculations on the side for area and perimeter
- A separate garden/yard section to the right
- Notes about materials and possible construction details

There are handwritten notes around the diagram that include:
- Area and perimeter formulas
- Calculations for different sections
- A "Garden" area shaded in green
- Annotations for walls, doors, and windows

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🧮 Key Elements & Problem Solving

Let’s analyze and solve the main mathematical components.

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#### ✔ 1. Total Area of the House

We can calculate the total area by summing up the areas of individual rooms or using the outer dimensions.

But first, let's identify the overall footprint of the house.

From the diagram:
- The main structure has a length of 15 m (labeled at bottom).
- The width varies due to irregular shape, but we can approximate or use the bounding rectangle.

However, there's an L-shaped layout, so we’ll divide it into rectangular parts.

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🔁 Divide the House into Rectangles

Let’s split the house into two main rectangular sections:

#### 🔹 Section A: Main Living Area
- Width: 8 m (horizontal dimension from left to right)
- Height: 10 m (vertical dimension)

> But wait — the height isn’t uniform. There's a 3m extension on top.

So better to split into three parts:

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🟦 Part 1: Bottom Rectangle (Living Room + Kitchen)

- Length: 15 m (from left to right)
- Height: 6 m (bottom part)
- Area = 15 × 6 = 90 m²

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🟨 Part 2: Top Left Rectangle (Bedroom or Study)

- Length: 8 m (left side)
- Height: 3 m (top extension)
- Area = 8 × 3 = 24 m²

Wait — actually, the top left has a 3m extension and 3m depth, but it's labeled as 8m wide? Let's check:

Looking closely:
- The top left room is 8m long (horizontal), 3m deep (vertical), so:
- Area = 8 × 3 = 24 m²

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🟩 Part 3: Top Right Rectangle (Another Room)

- This one is 3m wide, 3m high, but seems to be attached.
- Also, there's a 3m × 3m square near the top right, possibly a bedroom or bathroom.

But wait — there’s a 3m × 3m block on the top right labeled “Room 2”?

Actually, the top right has:
- A 3m × 3m room → Area = 9 m²

But this may not be correct — let’s look at the full outline.

Alternatively, perhaps the entire upper level is 10m wide (as labeled) and 3m deep, so:

- Upper section: 10m × 3m = 30 m²

Then lower section: 15m × 6m = 90 m²

But the lower section isn't fully 15m × 6m — there’s a recess on the right.

Let’s go back.

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🔎 Better Approach: Use Coordinates or Add Areas

Let’s list all rooms with dimensions:

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🏠 Room-by-Room Breakdown

1. Living Room (Main):
- 8m × 4m = 32 m²
*(From diagram: labeled "living room", 8m × 4m)*

2. Kitchen:
- 3m × 3m = 9 m²

3. Dining Area:
- 3m × 3m = 9 m²

4. Bedroom 1 (Top Left):
- 8m × 3m = 24 m²

5. Bedroom 2 (Top Right):
- 3m × 3m = 9 m²

6. Bathroom:
- 2m × 2m = 4 m²

7. Hallway / Corridor:
- Possibly 1m wide, length ~10m? Not clearly labeled.

But looking at the total outlined area, we can compute it as:

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✔ Total Area Calculation Using Outer Dimensions

Let’s consider the outer bounding box:

- Width: 15 m
- Height: 10 m (from bottom to top)
- So total area of bounding rectangle = 15 × 10 = 150 m²

But the house doesn’t fill the entire rectangle — there are cutouts and overhangs.

Alternatively, use addition method.

Let’s re-analyze the main structure:

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🧱 Structure Breakdown

The house appears to have:

- Bottom Part: 15m wide × 6m tall → 15 × 6 = 90 m²
- Top Part: 10m wide × 3m tall → 10 × 3 = 30 m²
- But the top part is not aligned — it extends over the bottom.

Wait — actually, the top left has a 3m × 3m extension, and the top right has another 3m × 3m room.

But looking at the red outline, the total shape is:

- Lower rectangle: 15m × 6m = 90 m²
- Upper rectangle: 10m × 3m = 30 m²
- But the upper rectangle overlaps the lower one? No — it's above.

Wait — no overlap. The upper section is only 10m wide, while the lower is 15m wide, so they are adjacent?

No — the upper section sits on top of the lower, but only 10m of the 15m width.

So the total area is:

- Lower: 15 × 6 = 90 m²
- Upper: 10 × 3 = 30 m²
- Total = 90 + 30 = 120 m²

But wait — the upper section includes two rooms:
- One is 8m × 3m = 24 m²
- Another is 3m × 3m = 9 m²
- And a small hallway?

Wait — the upper section is 10m wide and 3m deep, so area = 10 × 3 = 30 m²

And the lower section is 15m × 6m = 90 m²

But is the lower section really 15×6?

Looking at the diagram:
- From left to right: 15m
- From bottom to top: 6m for the base, then 3m more on top → total height 9m?

Wait — the height is marked as 10m at the top.

But the bottom is 6m, and the top extension is 3m → total height = 6 + 3 = 9m?

But it says 10m at the top.

Ah — maybe the top extension is 3m, and the bottom is 7m?

Let’s recheck.

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📐 Re-examining Dimensions

On the left side, vertical measurement:
- From bottom to top: 10m total
- Bottom section: 6m (labeled)
- Top section: 3m (labeled) → total = 9m → discrepancy.

Wait — maybe the top section is 4m?

No — the label says 3m.

Perhaps the bottom section is 7m?

Wait — the living room is labeled 6m high.

Let’s trust the labels.

From the right side:
- Vertical line shows: 6m (bottom), then 3m (top) → total 9m
- But the top of the house is labeled 10m — contradiction.

Wait — the top of the house is labeled 10m from the bottom, but the top extension is only 3m — so the bottom must be 7m?

No — the bottom is labeled 6m.

This suggests a mistake in labeling.

Alternatively, the 10m might be a total height including something else.

But likely, the total height is 9m, not 10m.

Possibly a typo.

Let’s assume:

- Bottom part: 15m × 6m = 90 m²
- Top part: 10m × 3m = 30 m²
- Total area = 90 + 30 = 120 m²

Now, subtract any overlaps or non-structural parts?

No — these are separate levels.

But the top part is not centered — it's offset.

But since we’re calculating floor area, we just add the footprint.

So total floor area = 120 m²

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🌿 Garden Area

On the right side, there's a garden shown as a green rectangle:

- Dimensions: 3m × 10m = 30 m²
- Labeled: "Garden – modeling fence"
- Perimeter: 2(3+10) = 26 m

Also, note: "P = 26 m" written nearby.

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🧮 Perimeter of House

To find the perimeter, trace the outer edge.

Start from bottom-left corner:

- Right: 15m
- Up: 6m
- Right: 3m (to align with top)
- Up: 3m
- Left: 10m
- Down: 3m
- Left: 3m
- Down: 6m

Wait — let’s trace carefully.

From bottom-left:
1. Right along bottom: 15 m
2. Up on right wall: 6 m
3. Then right? No — the top is only 10m wide, so there’s a recession.

Actually, the right side goes:
- Up 6m
- Then left 3m (into the house)
- Then up 3m
- Then left 10m
- Then down 3m
- Then left 3m
- Then down 6m
- Then left 15m

Wait — this is messy.

Better to use the outline:

The outer perimeter is:

- Bottom: 15 m
- Right side: from bottom to top — but it's not straight.

Actually, the house has:
- Bottom: 15 m
- Right side: 6 m (vertical)
- Then a horizontal inward to meet the top
- Then up 3 m
- Then left 10 m
- Then down 3 m
- Then left 3 m
- Then down 6 m
- Then left 15 m

Wait — this is double-counting.

Use coordinate geometry.

Assume origin at bottom-left.

Points:
1. (0,0)
2. (15,0) → bottom-right
3. (15,6) → up
4. (12,6) → left 3m
5. (12,9) → up 3m
6. (2,9) → left 10m
7. (2,6) → down 3m
8. (0,6) → left 2m? Wait — no.

Wait — the top starts at x=2? That doesn't make sense.

Look at the diagram:

- The top extension is 10m wide, and it's centered? Or shifted?

From the left side, the top left room is 8m wide, and the top right room is 3m wide → total 11m? But the total width is 15m.

Wait — the top section is 10m wide, so it must be centered?

But the left side shows a 3m extension.

Wait — the left side has:
- 3m horizontal extension at the top?
- Then 8m below?

No — the top left room is 8m wide and 3m deep.

The top right room is 3m wide and 3m deep.

So together: 8 + 3 = 11m wide.

But the bottom is 15m wide.

So the top section is 11m wide, not 10m.

Wait — the label says "10m" at the top — but the rooms are 8m and 3m → total 11m.

Contradiction.

Unless the 10m is a mistake.

Or the rooms are not adjacent.

Wait — there’s a gap between them?

No — the top section is drawn as a continuous strip.

But the left room is 8m wide, and the right room is 3m wide, with a hallway in between?

Yes — there’s a narrow corridor between them.

So total width = 8 + 1 (corridor) + 3 = 12m?

But the total width is labeled 10m — still inconsistent.

This suggests handwritten errors in labeling.

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✔ Best Estimate

Given the confusion in labels, let’s use clearly labeled rooms.

From the diagram:

| Room | Dimensions | Area |
|------|------------|------|
| Living Room | 8m × 4m | 32 m² |
| Kitchen | 3m × 3m | 9 m² |
| Dining | 3m × 3m | 9 m² |
| Bedroom 1 | 8m × 3m | 24 m² |
| Bedroom 2 | 3m × 3m | 9 m² |
| Bathroom | 2m × 2m | 4 m² |
| Hallways | approx. 10 m² | |

Sum: 32 + 9 + 9 + 24 + 9 + 4 + 10 = 107 m²

But this may miss some areas.

Alternatively, use outer dimensions:

- Main body: 15m × 6m = 90 m²
- Top extension: 10m × 3m = 30 m²
- Total: 120 m²

But if the top extension is only 10m, and the bottom is 15m, then the total area is 120 m², assuming no overlap.

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✔ Final Answers

#### 🏡 Total Floor Area of House:
≈ 120 m²

#### 🌿 Garden Area:
3m × 10m = 30 m²

#### 📐 Perimeter of House:
Trace the outer edge:
- Bottom: 15 m
- Right: 6 m
- Top right: 3 m
- Top: 10 m
- Top left: 3 m
- Left: 6 m
- But wait — the left side has a step.

Better:
- Start at (0,0)
- To (15,0): 15 m
- To (15,6): 6 m
- To (12,6): 3 m (left)
- To (12,9): 3 m (up)
- To (2,9): 10 m (left)
- To (2,6): 3 m (down)
- To (0,6): 2 m (left)
- To (0,0): 6 m (down)

Wait — this gives:
- 15 + 6 + 3 + 3 + 10 + 3 + 2 + 6 = 58 m

But the left side is 6m, and the top is 3m.

Wait — the left side has a vertical drop at 6m, then continues.

But the left wall is 6m high, then a 3m extension at the top.

So the perimeter is:

- Bottom: 15 m
- Right wall: 6 m
- Top right: 3 m
- Top: 10 m
- Top left: 3 m
- Left wall: 6 m
- But the left wall is only 6m high, so from (0,6) to (0,0): 6 m

But the top left has a projection — so the left side is not straight.

Actually, the outer edge is:

- (0,0) → (15,0) → (15,6) → (12,6) → (12,9) → (2,9) → (2,6) → (0,6) → (0,0)

So segments:
1. (0,0) to (15,0): 15 m
2. (15,0) to (15,6): 6 m
3. (15,6) to (12,6): 3 m
4. (12,6) to (12,9): 3 m
5. (12,9) to (2,9): 10 m
6. (2,9) to (2,6): 3 m
7. (2,6) to (0,6): 2 m
8. (0,6) to (0,0): 6 m

Sum: 15 + 6 + 3 + 3 + 10 + 3 + 2 + 6 = 58 m

✔ Perimeter = 58 m

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✔ Summary

| Quantity | Value |
|--------|-------|
| Total House Area | ≈ 120 m² |
| Garden Area | 30 m² |
| Perimeter of House | 58 m |
| Garden Perimeter | 2×(3+10) = 26 m |

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💡 Explanation

- The house is divided into a lower rectangle (15m × 6m) and an upper rectangle (10m × 3m).
- Total area = 90 + 30 = 120 m²
- The perimeter is calculated by tracing the outer edges, accounting for setbacks and projections.
- The garden is a simple rectangle: 3m × 10m = 30 m², with perimeter 26 m.

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If you have a specific question (e.g., "What is the area of the house?" or "How much fencing is needed?"), please clarify — but based on the image, this is the full solution.

Let me know if you want a digital version or a CAD-style redrawing!