Math worksheet for calculating area and perimeter of rectilinear shapes.

Let's solve each problem step by step. The key is to divide the rectilinear (L-shaped or stepped) shapes into rectangles, find missing sides using given dimensions, then calculate area (sum of rectangle areas) and perimeter (total outer edge length).

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🔢 Problem 1

Shape: L-shape with:
- Top rectangle: width = 5 cm, height = 6 cm
- Bottom rectangle: width = 8 cm, height = ? → total height is 7 cm, so bottom height = 7 - 6 = 1 cm

#### ➤ Area
Break into two rectangles:

- Top rectangle: 5 cm × 6 cm = 30 cm²
- Bottom rectangle: 8 cm × 1 cm = 8 cm²

✔ Total Area = 30 + 8 = 38 cm²

#### ➤ Perimeter
Trace the outer edges:

Start from top-left corner, go clockwise:

- Top: 5 cm
- Right side down: 7 cm
- Bottom: 8 cm
- Left side up: 1 cm (bottom part)
- Then up the inner vertical: 6 cm
- Then left across top of bottom rectangle: 8 - 5 = 3 cm

Wait — better to just add all outer sides:

Actually, easier way: add all horizontal and vertical outer segments.

Horizontal segments:
- Top: 5 cm
- Bottom: 8 cm
- Inner top of bottom rectangle: 3 cm (since 8 - 5 = 3)
→ Total horizontal = 5 + 8 + 3 = 16 cm? ✘ No — that’s double-counting.

Better method: trace the entire boundary.

Visualize path:

1. Start at top-left → right 5 cm
2. Down 7 cm
3. Left 8 cm
4. Up 1 cm (to inner corner)
5. Right 3 cm (to align under top rectangle)
6. Up 6 cm → back to start

So perimeter = 5 + 7 + 8 + 1 + 3 + 6 = 30 cm

✔ Perimeter = 30 cm

> ⚠️ Note: The worksheet says “Perimeter = ____ m” — this must be a typo! All units are in cm. We’ll answer in cm.

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✔ Answer for Problem 1:

- Area = 38 cm²
- Perimeter = 30 cm

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🔢 Problem 2

Shape: L-shape with:
- Overall width = 1 m
- Overall height = 0.9 m
- Right-top rectangle: height = 0.5 m, width = ? → total width 1 m, bottom-right part width = 0.4 m → so top width = 1 - 0.4 = 0.6 m

Bottom rectangle height = 0.9 - 0.5 = 0.4 m

#### ➤ Area
Break into two rectangles:

- Top rectangle: 0.6 m × 0.5 m = 0.3 m²
- Bottom rectangle: 1 m × 0.4 m = 0.4 m²

✔ Total Area = 0.3 + 0.4 = 0.7 m²

#### ➤ Perimeter
Trace outer boundary:

1. Top: 0.6 m
2. Right down: 0.5 m
3. Right-bottom: 0.4 m (horizontal)
4. Down: 0.4 m (vertical drop)
5. Left: 1 m
6. Up: 0.9 m

Wait — let’s do it properly:

Start top-left → right 0.6 m → down 0.5 m → right 0.4 m → down 0.4 m → left 1 m → up 0.9 m → back to start.

So perimeter = 0.6 + 0.5 + 0.4 + 0.4 + 1 + 0.9 = 3.8 m

But worksheet asks for mm!

Convert: 3.8 m = 3800 mm

✔ Perimeter = 3800 mm

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✔ Answer for Problem 2:

- Area = 0.7 m²
- Perimeter = 3800 mm

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🔢 Problem 3

Shape: L-shape with mixed units: cm and mm → convert everything to cm.

Given:
- Left side: 10 cm
- Top: 2 cm
- Right vertical: 55 mm = 5.5 cm
- Bottom horizontal: 60 mm = 6 cm

Find missing sides:

- Height of bottom rectangle = 10 - 5.5 = 4.5 cm
- Width of top rectangle = 2 cm
- Width of bottom rectangle = 6 cm → so inner horizontal segment = 6 - 2 = 4 cm

#### ➤ Area
Break into two rectangles:

- Top rectangle: 2 cm × 5.5 cm = 11 cm²
- Bottom rectangle: 6 cm × 4.5 cm = 27 cm²

✔ Total Area = 11 + 27 = 38 cm²

#### ➤ Perimeter
Trace outer boundary:

Start top-left → right 2 cm → down 5.5 cm → right 4 cm → down 4.5 cm → left 6 cm → up 10 cm → back to start.

Perimeter = 2 + 5.5 + 4 + 4.5 + 6 + 10 = 32 cm

✔ Perimeter = 32 cm

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✔ Answer for Problem 3:

- Area = 38 cm²
- Perimeter = 32 cm

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🔢 Problem 4

Shape: L-shape with:
- Overall width = 1.2 cm
- Overall height = 0.8 cm
- Bottom rectangle width = 1 cm → so top-right width = 1.2 - 1 = 0.2 cm
- Bottom rectangle height = 0.2 cm → so top rectangle height = 0.8 - 0.2 = 0.6 cm

#### ➤ Area
Break into two rectangles:

- Top rectangle: 1.2 cm × 0.6 cm = 0.72 cm²
- Bottom rectangle: 1 cm × 0.2 cm = 0.2 cm²

✔ Total Area = 0.72 + 0.2 = 0.92 cm²

#### ➤ Perimeter
Trace outer boundary:

Start top-left → right 1.2 cm → down 0.8 cm → left 1 cm → up 0.2 cm → left 0.2 cm → up 0.6 cm → back to start.

Wait — let’s list segments:

1. Top: 1.2 cm
2. Right: 0.8 cm
3. Bottom: 1 cm
4. Up inner vertical: 0.2 cm
5. Left inner horizontal: 0.2 cm
6. Up to top: 0.6 cm

Perimeter = 1.2 + 0.8 + 1 + 0.2 + 0.2 + 0.6 = 4.0 cm

✔ Perimeter = 4.0 cm

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✔ Answer for Problem 4:

- Area = 0.92 cm²
- Perimeter = 4.0 cm

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## 📝 Final Answers:

1)

- Area = 38 cm²
- Perimeter = 30 cm

2)

- Area = 0.7 m²
- Perimeter = 3800 mm

3)

- Area = 38 cm²
- Perimeter = 32 cm

4)

- Area = 0.92 cm²
- Perimeter = 4.0 cm

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✔ All solved by dividing into rectangles, finding missing sides, computing area as sum of rectangle areas, and perimeter as total outer edge length. Units carefully converted where needed.