Area Of Irregular Shapes Worksheet - Free Printable

Let's solve each of the four rectilinear shapes by breaking them into rectangles, calculating the area of each rectangle, and then adding them together.

---

🔷 Shape 1

```
3cm
+-------+
| |
1cm | |
| |
+---+---+
| |
2cm | |
+---+
```

We can split this shape into two rectangles:

- Rectangle A (top):
Width = 3 cm, Height = 1 cm
Area = 3 × 1 = 3 cm²

- Rectangle B (bottom):
Width = 3 cm, Height = 2 cm
Area = 3 × 2 = 6 cm²

✔ Total Area = 3 + 6 = 9 cm²

---

🔷 Shape 2

```
+--------+
| |
6cm | |
| |
+----+---+
| |
4cm | |
+---+
2cm
```

Split into two rectangles:

- Rectangle A (left):
Width = 4 cm, Height = 6 cm
Area = 4 × 6 = 24 cm²

- Rectangle B (right):
Width = 2 cm, Height = 4 cm
Area = 2 × 4 = 8 cm²

✔ Total Area = 24 + 8 = 32 cm²

---

🔷 Shape 3

```
+-----------+
| |
2cm | |
| |
+-----+-----+
| | |
3cm | | |
| | |
+-----+-----+
6cm
```

Wait — let’s analyze carefully.

The total width is 6 cm. The top part has a step of 2 cm on the left.

So we can split it into:

- Rectangle A (bottom):
Width = 6 cm, Height = 3 cm
Area = 6 × 3 = 18 cm²

- Rectangle B (top right):
Width = (6 - 2) = 4 cm, Height = (4 - 3) = 1 cm
But wait — actually, the full height on the right is 4 cm, and bottom is 3 cm, so the top extension is only 1 cm high.

But looking at the diagram:

- The bottom rectangle is 6 cm wide × 3 cm high → Area = 6 × 3 = 18 cm²
- The top rectangle is (6 - 2) = 4 cm wide × 1 cm high → Area = 4 × 1 = 4 cm²

✔ Total Area = 18 + 4 = 22 cm²

> ✔ Alternative: Think of it as a large rectangle of 6×4 minus a small rectangle missing? No — actually, it's added.

Yes, correct: 22 cm²

---

🔷 Shape 4

```
+------------------+
| |
5cm | |
| |
+---------+--------+
| |
6cm | |
| |
+--------+
10cm
```

Wait — labels:

- Total base = 10 cm
- Left part: width = 6 cm, height = 5 cm
- Right part: width = (10 - 6) = 4 cm, height = 2 cm

So split into:

- Rectangle A (left):
Width = 6 cm, Height = 5 cm
Area = 6 × 5 = 30 cm²

- Rectangle B (right):
Width = (10 - 6) = 4 cm, Height = 2 cm
Area = 4 × 2 = 8 cm²

✔ Total Area = 30 + 8 = 38 cm²

---

✔ Final Answers:

1) 9 cm²
2) 32 cm²
3) 22 cm²
4) 38 cm²

---

📌 Summary:

| Shape | Area (cm²) |
|------|------------|
| 1 | 9 |
| 2 | 32 |
| 3 | 22 |
| 4 | 38 |

Let me know if you'd like visual breakdowns or diagrams!