Math worksheet for calculating total area of irregular shapes with step-by-step instructions.

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.

---

Problem 1: First Shape

```
3m
+-----+
| |
5m | | 3m
| +-----+
| |
| | 3m
+-----------+
```

This shape can be split into two rectangles:

- Rectangle A1: Left part — height = 5m, width = 3m
→ Area = 5 × 3 = 15 m²

- Rectangle A2: Right part — height = 3m, width = 3m
→ Area = 3 × 3 = 9 m²

Total Area = 15 + 9 = 24 m²

✔ Fill in:
- A1 = 5 × 3
- A2 = 3 × 3
- Total Area = 24 m²

---

Problem 2: Second Shape

```
10m
+--------+
| |
8m| |10m
| |
| +----+
| | |
| | 4m |
| +----+
+--------+
```

This shape has a taller left section and a shorter right one.

Split it into:

- Rectangle A1: Left part — height = 8m, width = 4m
→ Area = 8 × 4 = 32 m²

- Rectangle A2: Right part — height = 10m, width = (10 - 4) = 6m
→ Area = 10 × 6 = 60 m²

Wait! Actually, let’s look again.

The total width is 10m, and the left part is 4m wide. So the right part is 10 − 4 = 6m wide.

But the height of the right part is 10m, and the left part is 8m tall. So we need to adjust.

Actually, this shape looks like a rectangle with a smaller rectangle attached on top or side?

Looking carefully:

It seems like a large rectangle (10m wide, 10m high), but there's a step down on the left side.

Wait — better way: divide it into two rectangles:

- A1: Bottom-left rectangle — 8m tall, 4m wide → 8 × 4 = 32 m²
- A2: Remaining part — This includes the full right side and the top of the left side.

But actually, from the diagram:

- The left part is 4m wide and 8m tall.
- The right part is 6m wide (since 10 - 4 = 6) and 10m tall.

So:

- A1 = 8 × 4 = 32 m²
- A2 = 10 × 6 = 60 m²

Total Area = 32 + 60 = 92 m²

✔ Fill in:
- A1 = 8 × 4
- A2 = 10 × 6
- Total Area = 92 m²

---

Problem 3: Third Shape (House Floor Plan)

```
5m
+------+
| |
12m| |7m
| +------+
| |
| | 5m
+-------------+
```

This is a house-shaped figure with a tall rectangle on the left and a smaller one on the right.

Break it into two rectangles:

- A1: Left rectangle — height = 12m, width = 5m
→ Area = 12 × 5 = 60 m²

- A2: Right rectangle — height = 5m, width = 7m
→ Area = 5 × 7 = 35 m²

Total Area = 60 + 35 = 95 m²

✔ Fill in:
- A1 = 12 × 5
- A2 = 5 × 7
- Total Area = 95 m²

---

✔ Final Answers:

#### First Shape
- A1 = 5 × 3
- A2 = 3 × 3
- Total Area = 24 m²

#### Second Shape
- A1 = 8 × 4
- A2 = 10 × 6
- Total Area = 92 m²

#### Third Shape (Carpet)
- A1 = 12 × 5
- A2 = 5 × 7
- Total Area = 95 m²

> ✔ So, 95 square metres of carpet are laid in this house.

---

📝 Summary:

| Shape | A1 | A2 | Total Area |
|-------|-----|-----|------------|
| 1 | 5×3 | 3×3 | 24 m² |
| 2 | 8×4 | 10×6 | 92 m² |
| 3 | 12×5 | 5×7 | 95 m² |

And the answer to the question:
👉 How many square metres of carpet are laid in this house?
→ 95 m² ✔