Area and Perimeter Project Based Learning - Free Printable

Let's solve the Area and Perimeter Floor Plan Project step by step. We are given a floor plan divided into rooms, each with labeled dimensions in "units." Our goal is to calculate:

1. Area of each room (in square units)
2. Perimeter of each room (in units)
3. Possibly the total area and perimeter of the entire house (if required)

We'll go room by room.

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🔹 Step 1: Understand the Grid

Each small square on the grid represents 1 unit × 1 unit, so:
- Area = length × width (in square units)
- Perimeter = 2 × (length + width) (in units)

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🔸 Room 1: Living Room

- Dimensions: 7 units (width) × 8 units (height)
- Area = 7 × 8 = 56 square units
- Perimeter = 2 × (7 + 8) = 2 × 15 = 30 units

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🔸 Room 2: Bedroom 1

- Dimensions: 6 units (width) × 6 units (height)
- Area = 6 × 6 = 36 square units
- Perimeter = 2 × (6 + 6) = 2 × 12 = 24 units

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🔸 Room 3: Bedroom 2

- Dimensions: 5 units (width) × 8 units (height)
- Area = 5 × 8 = 40 square units
- Perimeter = 2 × (5 + 8) = 2 × 13 = 26 units

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🔸 Room 4: Bathroom

- Dimensions: 3 units (width) × 4 units (height)
*(Note: From the grid, it spans 3 units wide and 4 units tall)*
- Area = 3 × 4 = 12 square units
- Perimeter = 2 × (3 + 4) = 2 × 7 = 14 units

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🔸 Room 5: Kitchen

- Dimensions: 5 units (width) × 6 units (height)
- Area = 5 × 6 = 30 square units
- Perimeter = 2 × (5 + 6) = 2 × 11 = 22 units

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🔸 Room 6: Hall

- Dimensions: 8 units (width) × 2 units (height)
- Area = 8 × 2 = 16 square units
- Perimeter = 2 × (8 + 2) = 2 × 10 = 20 units

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✔ Summary Table

| Room | Length | Width | Area (sq units) | Perimeter (units) |
|---------------|--------|-------|------------------|--------------------|
| Living Room | 8 | 7 | 56 | 30 |
| Bedroom 1 | 6 | 6 | 36 | 24 |
| Bedroom 2 | 8 | 5 | 40 | 26 |
| Bathroom | 4 | 3 | 12 | 14 |
| Kitchen | 6 | 5 | 30 | 22 |
| Hall | 2 | 8 | 16 | 20 |

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🧮 Total Area of the House

Add all areas:
> 56 + 36 + 40 + 12 + 30 + 16 = 190 square units

✔ Total Area = 190 sq units

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🧮 Total Perimeter of the Entire House?

To find the outer perimeter of the whole house, we need to look at the outer edges of the entire shape.

From the diagram:
- The full height of the house: Top part is 8 units, bottom is 8 units → total 14 units high
- The full width: Left side is 7 units (living room), then 6 units (bedroom 1), but they're stacked differently.

Wait — let’s examine the overall bounding box:

Looking at the grid:
- Width: From leftmost edge to rightmost edge:
- Living room: 7 units
- Bedroom 1: 6 units
- But they are side-by-side? No — actually, the living room is on the left, bedroom 1 on the right.
- However, the total width from left to right:
- Left edge: starts at column 0
- Right edge: ends at column 7 + 6 = 13 units wide? Let’s count columns.

But better: Use the grid lines.

From the image:
- Bottom row: Bedroom 2 (5), Bathroom (3), Kitchen (5) → total width = 5+3+5 = 13 units
- Top: Living room (7) and Bedroom 1 (6) → but they are aligned such that the total width is 7 + 6 = 13 units → matches.

Height:
- Top: Living room and Bedroom 1 both 8 units tall → top half is 8 units
- Bottom: Bedroom 2 and others are 8 units tall
- But Hall is only 2 units high → so total height is 8 (top) + 6 (bottom)? Wait no.

Wait — let’s analyze vertical layout:

- The top two rooms (Living Room and Bedroom 1) are 8 units high
- The bottom section (Bedroom 2, Bathroom, Kitchen, Hall) is 6 units high?
- But Hall is only 2 units high, and below it are 6 units for kitchen and bathroom?

Wait — actually, looking at the labels:
- On the left side, the total height is labeled as:
- 8 units (top) + 8 units (bottom) = 16 units high
- On the right side, it’s labeled as:
- 6 units (top) + 6 units (bottom) = 12 units high?

That doesn't match.

Wait — this suggests the house is not rectangular — it has an irregular shape.

So we can’t just use a rectangle. We must trace the outer boundary.

Let’s reconstruct the entire outline.

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🔎 Trace the Outer Perimeter

We’ll go around the outside of the house.

Start from the bottom-left corner and move clockwise.

#### Step-by-step tracing:

1. Bottom edge:
- From left to right: Bedroom 2 (5), Bathroom (3), Kitchen (5) → total 13 units

2. Right edge:
- From bottom to top:
- Kitchen: 6 units up
- Then Hall: 2 units up
- Then Bedroom 1: 6 units up
- So total right side: 6 + 2 + 6 = 14 units

But wait — is that correct?

Let’s check vertical alignment.

- Left side:
- Living Room: 8 units tall
- Bedroom 2: 8 units tall
- So total left side: 8 + 8 = 16 units

- Right side:
- Bedroom 1: 6 units tall
- Hall: 2 units tall
- Kitchen: 6 units tall
- So total: 6 + 2 + 6 = 14 units

But this is inconsistent — the house is not symmetrical.

Actually, from the grid:

- Top edge:
- Living Room: 7 units wide
- Bedroom 1: 6 units wide
- Total top width: 7 + 6 = 13 units

- Bottom edge:
- Bedroom 2: 5
- Bathroom: 3
- Kitchen: 5
- Total: 5 + 3 + 5 = 13 units

- Left edge:
- Living Room: 8 units high
- Bedroom 2: 8 units high
- Total: 16 units

- Right edge:
- Bedroom 1: 6 units high
- Hall: 2 units high
- Kitchen: 6 units high
- Total: 6 + 2 + 6 = 14 units

But this means the house has an overhang on the left — it extends higher than the right.

So the outer perimeter must be traced carefully.

Let’s define coordinates.

Assume bottom-left corner is (0,0).

Now map each room:

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📐 Coordinates and Shape

Let’s define the bounding box and outline.

From the grid:

- Living Room:
- Bottom-left: (0, 8) → top-right: (7, 16) → height 8, width 7
- Bedroom 1:
- Bottom-left: (7, 8) → top-right: (13, 14) → width 6, height 6
- Bedroom 2:
- Bottom-left: (0, 0) → top-right: (5, 8) → width 5, height 8
- Bathroom:
- Bottom-left: (5, 0) → top-right: (8, 4) → width 3, height 4
- Kitchen:
- Bottom-left: (8, 0) → top-right: (13, 6) → width 5, height 6
- Hall:
- Bottom-left: (5, 4) → top-right: (13, 6) → width 8, height 2

Wait — Hall is above Bathroom and Kitchen, from x=5 to x=13 (8 units), y=4 to y=6 (2 units)

So now we can trace the outer boundary.

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✔ Outer Perimeter Tracing

Start at (0,0) → bottom-left

1. Go right along bottom edge:
- From (0,0) to (13,0): 13 units

2. Up the right side:
- From (13,0) to (13,6): Kitchen → 6 units
- Then Hall: (13,6) to (13,8): 2 units
- Then Bedroom 1: (13,8) to (13,14): 6 units
- But wait — Bedroom 1 goes from y=8 to y=14? That would be 6 units high, yes.
- But Living Room goes to y=16, so we have a gap?

Wait — Living Room is from y=8 to y=16 → height 8 → so top is at y=16
- Bedroom 1 is from y=8 to y=14 → height 6 → so it stops at y=14

So at x=13:
- From y=0 to y=6: Kitchen
- y=6 to y=8: Hall
- y=8 to y=14: Bedroom 1
- Then from y=14 to y=16: no room — but Living Room is on the left!

So the top-right corner is not at (13,16). Instead, the roofline is stepped.

So the outer edge is not straight.

We need to trace the actual outer path.

Let’s do it step by step.

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🚶‍♂️ Clockwise Perimeter Path

Start at (0,0)

1. Right along bottom: (0,0) → (13,0): 13 units

2. Up along right wall:
- (13,0) → (13,6): Kitchen → 6 units
- (13,6) → (13,8): Hall → 2 units
- (13,8) → (13,14): Bedroom 1 → 6 units
- Now at (13,14)

But Living Room ends at y=16, so from (13,14) to (13,16)? No — Living Room is only from x=0 to x=7, so no wall at x=13 from y=14 to y=16.

So after (13,14), we must go left to connect to Living Room.

Actually, the top edge of the house:
- From x=0 to x=7: Living Room → top at y=16
- From x=7 to x=13: Bedroom 1 → top at y=14

So the roofline is:
- Horizontal from (0,16) to (7,16)
- Then down to (7,14) → but wait — is there a wall?

Actually, no wall between Living Room and Bedroom 1 — they are adjacent.

But the outer edge must follow the outside.

So from (13,14), we go left along the top of Bedroom 1 to (7,14)

Then up to (7,16) — because Living Room goes up to y=16

Then left to (0,16)

Then down to (0,0)

Wait — but from (0,16) to (0,0) is the left wall?

Yes — left wall is 16 units high.

But earlier we said Bedroom 2 is from y=0 to y=8, so from (0,0) to (0,8) is wall

Then from (0,8) to (0,16): Living Room wall

So yes — left wall is continuous from y=0 to y=16.

So let’s trace:

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✔ Final Perimeter Path (Clockwise)

1. Start at (0,0)

2. → (13,0): 13 units (bottom)

3. → (13,6): 6 units (right side of kitchen)

4. → (13,8): 2 units (right side of hall)

5. → (13,14): 6 units (right side of bedroom 1)

6. → (7,14): 6 units (top of bedroom 1 — horizontal)

7. → (7,16): 2 units (vertical up to top of living room)

8. → (0,16): 7 units (top of living room)

9. → (0,0): 16 units (left wall)

Wait — from (0,16) to (0,0) is 16 units — yes.

But is that correct? Let’s add segments:

- (0,0) → (13,0): 13
- (13,0) → (13,6): 6
- (13,6) → (13,8): 2
- (13,8) → (13,14): 6
- (13,14) → (7,14): 6
- (7,14) → (7,16): 2
- (7,16) → (0,16): 7
- (0,16) → (0,0): 16

Wait — but (0,16) to (0,0) is 16 units, but that’s the left wall — yes.

But now sum:

- 13 + 6 + 2 + 6 + 6 + 2 + 7 + 16 = ?

Calculate:

13 + 6 = 19
19 + 2 = 21
21 + 6 = 27
27 + 6 = 33
33 + 2 = 35
35 + 7 = 42
42 + 16 = 58 units

But wait — this includes internal walls? No — we are tracing only the outer edge.

But we went from (13,14) to (7,14) — is that external?

No! That’s internal — it’s the shared wall between Bedroom 1 and Living Room.

We should not include internal walls.

So the true outer perimeter must not go through internal walls.

So the correct way is:

After (13,14), instead of going left to (7,14), we go up? No — there’s no wall.

Actually, the roofline is:
- From (7,16) to (13,14) — but that’s diagonal? No — it's stepped.

The outer boundary is:
- At the top:
- From (0,16) to (7,16): top of living room
- Then from (7,16) to (7,14): down the right side of living room? But no — living room ends at x=7, and bedroom 1 starts at x=7, but bedroom 1 only goes to y=14.

So the roofline is:
- From (0,16) to (7,16): flat
- Then from (7,16) to (13,14): but that’s not a wall — it’s open.

Wait — actually, the outer edge is only where there is a wall.

So the top edge:
- From (0,16) to (7,16): wall (top of living room)
- Then from (7,16) to (13,14): no wall — it’s exposed air
- But the right side of bedroom 1 is at x=13, from y=8 to y=14

So the outer perimeter must go:
- (0,0) → (13,0) → (13,14) → (7,14) → (7,16) → (0,16) → (0,0)

But again, (13,14) to (7,14) is horizontal — but is that exposed?

No — it’s internal if there’s a wall between them.

But there is no wall between Living Room and Bedroom 1 — they are adjacent, but the outer wall is only on the far sides.

So the outer boundary is:

- Bottom: (0,0) to (13,0) → 13
- Right: (13,0) to (13,14) → 14 units
- Then top-right corner is (13,14)
- But the top of Living Room is at (7,16), so we need to go from (13,14) to (7,16)? That’s diagonal — not possible.

Wait — the correct outer path is:

- Start at (0,0)
- → (13,0): 13
- → (13,14): 14 (right wall)
- → (7,14): 6 (top of bedroom 1 — but this is internal!)
- → (7,16): 2 (up)
- → (0,16): 7 (top of living room)
- → (0,0): 16 (left wall)

But (13,14) to (7,14) is not external — it’s inside the house.

So we cannot go there.

Instead, the outer edge must go from (13,14) to (13,16)? But no room there.

Ah — here’s the issue: the house has a recess on the right side.

The highest point is at (0,16) and (7,16), but the right side only goes to (13,14).

So the roofline is:
- From (7,16) to (13,14): but no wall — so the outer edge is only the walls.

So the true outer perimeter is:

1. (0,0) → (13,0): 13
2. (13,0) → (13,6): 6 (kitchen)
3. (13,6) → (13,8): 2 (hall)
4. (13,8) → (13,14): 6 (bedroom 1)
5. (13,14) → (13,16): ??? — no room above

Wait — there is no room above bedroom 1, so the wall ends at y=14.

Similarly, living room goes to y=16, so at x=7, from y=14 to y=16, there is a wall.

But at x=7, from y=14 to y=16, it's the right side of living room.

And at x=13, from y=14 to y=16, there is no wall.

So the outer edge is:

- After (13,14), we go left to (7,14)? No — that's internal.

Actually, the top of the house is:
- From (0,16) to (7,16): wall
- From (7,16) to (7,14): wall (right side of living room)
- From (7,14) to (13,14): wall? No — it's the top of bedroom 1, but bedroom 1 is at x=7 to x=13, y=8 to y=14, so its top is at y=14.

But the top edge of bedroom 1 is not external — it's shared with the space above.

So the only external walls are:
- Bottom: (0,0) to (13,0)
- Right: (13,0) to (13,14)
- Top: (13,14) to (7,14)? No — that's not external.

Wait — I think the best way is to realize that the outer perimeter is the boundary of the union of all rooms.

From the grid, the entire shape has:

- Left side: x=0, from y=0 to y=16 → 16 units
- Right side: x=13, from y=0 to y=14 → 14 units
- Bottom: y=0, from x=0 to x=13 → 13 units
- Top: y=16, from x=0 to x=7 → 7 units
- Then from (7,16) to (13,14): diagonal? No — it's stepped.

Actually, the top edge is:
- From (0,16) to (7,16): 7 units
- Then from (7,16) to (7,14): 2 units down (wall)
- Then from (7,14) to (13,14): 6 units right (top of bedroom 1)
- Then from (13,14) to (13,0): 14 units down

But (7,14) to (13,14) is external only if there is no room above — yes, there is no room above bedroom 1, so the top of bedroom 1 is external.

Similarly, the top of living room is external.

So the outer perimeter is:

1. (0,0) → (13,0): 13
2. (13,0) → (13,14): 14
3. (13,14) → (7,14): 6
4. (7,14) → (7,16): 2
5. (7,16) → (0,16): 7
6. (0,16) → (0,0): 16

Now sum:
- 13 + 14 = 27
- +6 = 33
- +2 = 35
- +7 = 42
- +16 = 58 units

But wait — we double-counted or included internal?

No — all these are external walls.

- (13,14) to (7,14): this is the top of bedroom 1, which is exposed — yes, external
- (7,14) to (7,16): right side of living room — external
- (7,16) to (0,16): top of living room — external
- (0,16) to (0,0): left wall — external
- (0,0) to (13,0): bottom — external
- (13,0) to (13,14): right wall — external

Yes — this is the full outer perimeter.

So Perimeter = 13 + 14 + 6 + 2 + 7 + 16 = 58 units

✔ Total Perimeter = 58 units

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✔ Final Answers

#### Individual Rooms:

| Room | Area (sq units) | Perimeter (units) |
|--------------|------------------|--------------------|
| Living Room | 56 | 30 |
| Bedroom 1 | 36 | 24 |
| Bedroom 2 | 40 | 26 |
| Bathroom | 12 | 14 |
| Kitchen | 30 | 22 |
| Hall | 16 | 20 |

#### Total:
- Total Area = 190 square units
- Total Perimeter = 58 units

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✔ Summary

This floor plan project teaches:
- How to calculate area and perimeter of rectangles
- How to combine rooms to find total area
- How to trace irregular shapes to find outer perimeter

Let me know if you'd like a printable version or graph paper version!