Worksheet for calculating the area of irregular shapes by breaking them into rectangles.

Let's solve each of the irregular shapes step by step. The goal is to break each shape into rectangles, calculate the area of each rectangle, and then add them together to find the total area.

We’ll use the formula:
Area = length × width

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🔹 Problem 1:

This shape can be split into two rectangles:

- Rectangle A: Top part
- Length = 6.4 m
- Width = 4.3 m
- Area = 6.4 × 4.3 = 27.52 m²

- Rectangle B: Bottom part
- Length = 2.1 m
- Width = 3.4 m
- Area = 2.1 × 3.4 = 7.14 m²

✔ Total Area = 27.52 + 7.14 = 34.66 m²

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🔹 Problem 2:

Split into two rectangles:

- Rectangle A: Left side
- Height = 5 m (from bottom to top)
- Width = 7.8 m
- Area = 5 × 7.8 = 39.0 m²

- Rectangle B: Right extension
- Height = 7.2 m – 5 m = 2.2 m
- Width = 3.2 m
- Area = 2.2 × 3.2 = 7.04 m²

✔ Total Area = 39.0 + 7.04 = 46.04 m²

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🔹 Problem 3:

This shape has a "step" in it. We can split it into three rectangles or two rectangles. Let's do two:

#### Option: Split vertically at 5.3 m

- Rectangle A: Left part
- Width = 4.7 m
- Height = 12.8 m
- Area = 4.7 × 12.8 = 60.16 m²

- Rectangle B: Right part
- Width = 4.3 m
- Height = 5.3 m
- Area = 4.3 × 5.3 = 22.79 m²

But wait — there’s also a bottom section that extends below the 5.3 m?

Wait! Let's re-analyze carefully.

Actually, this shape looks like:
- A large vertical rectangle on the left: 12.8 m tall × 4.7 m wide
- On the right, a smaller rectangle attached at the top: 4.3 m wide × 5.3 m tall
- But there’s a gap? No — actually, the bottom part has an overhang.

Wait — look at the numbers:

- Total height on left: 12.8 m
- Then a horizontal line at 5.3 m above the bottom?
- And a small rectangle on the right: 4.3 m wide, but only 5.3 m high?

Wait — let’s label from bottom up:

From the diagram:
- Bottom rectangle: 4.7 m wide × 12.8 m tall → that's one piece.
- But there’s a smaller rectangle on the right, extending upward from 5.3 m to 12.8 m?

No — actually, the figure shows:

- The left side goes up to 12.8 m.
- The right side starts at 5.3 m and goes up to 12.8 m? That doesn’t make sense.

Wait — perhaps better to break into two rectangles:

#### Rectangle 1: The full base
- Width = 4.7 m + 4.3 m = 9.0 m
- Height = 5.3 m
- Area = 9.0 × 5.3 = 47.7 m²

#### Rectangle 2: The top part (only on the right)
- Width = 4.3 m
- Height = 12.8 m – 5.3 m = 7.5 m
- Area = 4.3 × 7.5 = 32.25 m²

✔ Total Area = 47.7 + 32.25 = 79.95 m²

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🔹 Problem 4:

This is a more complex shape. Let’s analyze.

It looks like:
- A long horizontal rectangle at the bottom: 8.2 m tall, width = 3.7 + 5.1 + 5.1 + 3.7 = 17.6 m
- But wait — no. There's a step in the middle.

Better approach: Split into three rectangles.

#### Rectangle A: Left side (bottom)
- Width = 3.7 m
- Height = 8.2 m
- Area = 3.7 × 8.2 = 30.34 m²

#### Rectangle B: Middle section (bottom)
- Width = 5.1 m
- Height = 8.2 m – 3.7 m? Wait — no.

Wait — look at the labels:

- The bottom has:
- Left: 3.7 m wide, height = 8.2 m
- Middle: 5.1 m wide, height = 8.2 m
- Right: 3.7 m wide, height = 8.2 m

But wait — there’s a middle step.

Actually, the shape has:
- A long bottom rectangle of 3.7 + 5.1 + 5.1 + 3.7 = 17.6 m wide, but height only 3.7 m?
No — wait.

Let’s read the dimensions carefully:

From the image:

- The bottom of the shape has:
- Left: 3.7 m wide, height = 8.2 m
- Middle: 5.1 m wide, but height = ? — actually, the middle is raised.
- Right: 3.7 m wide, height = 8.2 m

But the top of the shape has a flat section: 12.6 m wide, and height = 8.2 m

Wait — here’s the correct way:

The shape has:
- A base of 3.7 + 5.1 + 5.1 + 3.7 = 17.6 m wide, but only 3.7 m high? No.

Wait — actually, the bottom layer is only 3.7 m high.

Then above it, there's a middle layer of 5.1 + 5.1 = 10.2 m wide, height = 8.2 – 3.7 = 4.5 m?

Wait — no. The total height is 8.2 m.

Look at the labels:
- Bottom: 3.7 m
- Then a step up to 8.2 m

Wait — the entire height is 8.2 m, and there are two levels.

Let’s define:

#### Rectangle 1: Bottom base (full width)
- Width = 3.7 + 5.1 + 5.1 + 3.7 = 17.6 m
- Height = 3.7 m
- Area = 17.6 × 3.7 = 65.12 m²

#### Rectangle 2: Top part (middle section)
- Width = 5.1 + 5.1 = 10.2 m
- Height = 8.2 – 3.7 = 4.5 m
- Area = 10.2 × 4.5 = 45.9 m²

✔ Total Area = 65.12 + 45.9 = 111.02 m²

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✔ Final Answers:

1. 34.66 m²
2. 46.04 m²
3. 79.95 m²
4. 111.02 m²

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✔ Summary:

| Problem | Area |
|--------|------|
| 1 | 34.66 m² |
| 2 | 46.04 m² |
| 3 | 79.95 m² |
| 4 | 111.02 m² |

All answers include units as requested.