Worksheet for calculating the area of compound shapes with six examples and a QR code for video instructions.

Let's solve Question 1 from the image:
We are asked to find the area of each compound shape (a) through (f). Each shape is made up of rectangles, so we can break them down into simpler rectangles, calculate their areas, and then add or subtract as needed.

---

🔷 Strategy:

- Break each shape into rectangles.
- Find the area of each rectangle using:
$$
\text{Area} = \text{length} \times \text{width}
$$
- Add areas for shapes made of multiple rectangles.
- Subtract areas if a part is missing (like in shape (e) and (f)).

---

## ✔ (a)

```
9cm
┌────────────┐
│ │
│ 8cm │
│ │
├─────┬──────┤
│ │ │
│ 5cm │ │
│ │ │
└─────┴──────┘
7cm
```

Break it into two rectangles:

1. Top rectangle: width = 9 cm, height = 8 cm → Area = $9 \times 8 = 72\,\text{cm}^2$

2. Bottom rectangle: width = 7 cm, height = 5 cm → Area = $7 \times 5 = 35\,\text{cm}^2$

But wait! The bottom rectangle doesn't extend across the full width — actually, the total base is 7 cm, but the top is 9 cm, so there’s an overhang.

Wait — let's re-analyze carefully.

Looking at the diagram:
- The total height is 8 cm.
- There's a step down of 5 cm on the right side.
- So the left part is a tall rectangle (height 8 cm), and the right part is shorter (height 5 cm).

Actually, better to split vertically.

Split into:
- Left rectangle: width = 5 cm (since the step is 5 cm wide), height = 8 cm → $5 \times 8 = 40\,\text{cm}^2$
- Right rectangle: width = 7 cm, height = 5 cm → $7 \times 5 = 35\,\text{cm}^2$

Wait — but the top is 9 cm wide, and the bottom is 7 cm wide. That means the left part is 9 cm wide at the top, but only 7 cm at the bottom? No — that doesn’t make sense.

Wait — let's look again.

Actually, the shape looks like this:

- Top horizontal segment: 9 cm wide, 8 cm high.
- Then a step down on the right: the lower part extends only 7 cm horizontally, but the vertical drop is 5 cm.

So the vertical drop is 5 cm, meaning the lower section has height 5 cm, and the upper section has height $8 - 5 = 3$ cm?

Wait — no, the total height is 8 cm, and the lower part is 5 cm high, so upper part must be $8 - 5 = 3$ cm high?

But the label says "8cm" on the side — that's the total height.

Let me clarify with dimensions:

From the diagram:
- Total height = 8 cm
- Lower rectangle height = 5 cm → so upper rectangle height = $8 - 5 = 3$ cm
- Upper rectangle width = 9 cm → area = $9 \times 3 = 27\,\text{cm}^2$
- Lower rectangle width = 7 cm → area = $7 \times 5 = 35\,\text{cm}^2$

Now, total area = $27 + 35 = 62\,\text{cm}^2$

✔ Answer (a): 62 cm²

---

## ✔ (b)

```
25cm
┌────────────┐
│ │
│ 12cm │
│ │
├─────┬──────┤
│ │ │
│10cm │ 6cm │
│ │ │
└─────┴──────┘
```

This is a T-shape.

Break it into:
- Top rectangle: width = 25 cm, height = 12 cm → $25 \times 12 = 300\,\text{cm}^2$
- Bottom rectangle: width = 6 cm, height = 10 cm → $6 \times 10 = 60\,\text{cm}^2$

But wait — the top rectangle is only 12 cm tall, and the bottom is 10 cm tall, but they’re stacked? Actually, the total height is 12 cm on top, and the stem goes down 10 cm, but the stem is centered?

Wait — looking at the diagram:

- The top rectangle is 25 cm wide, 12 cm tall.
- Below it, there’s a stem of width 6 cm and height 10 cm, centered under the top.

But wait — the total height is not additive unless they're stacked.

Actually, the top part is 12 cm tall, and the stem is 10 cm tall, but the stem is below the top? Or is the stem part of the same height?

Wait — the 12 cm is the total height of the whole shape?

No — the label shows:
- Top: 12 cm height
- Then below, the stem is 10 cm tall

But that would make total height = 12 + 10 = 22 cm? But that seems inconsistent.

Wait — no: the 12 cm is the height of the top rectangle, and the stem is below it, 10 cm tall, so total height = 12 + 10 = 22 cm?

But the diagram labels the entire shape as having a vertical dimension of 12 cm? Wait — no.

Wait — the label "12cm" is on the side of the top rectangle, and the stem is labeled 10 cm, and the width of the stem is 6 cm.

So the shape is:
- A large rectangle: 25 cm wide × 12 cm tall
- Then a smaller rectangle below it: 6 cm wide × 10 cm tall, centered

But wait — that would mean the total height is 12 + 10 = 22 cm, but the diagram doesn’t show that.

Alternatively, maybe the 12 cm is the total height, and the stem is 10 cm tall, so the top is only $12 - 10 = 2$ cm tall?

But that contradicts the labeling.

Wait — the 12 cm is labeled next to the top rectangle, and the 10 cm is labeled next to the stem, and they are stacked, so total height is $12 + 10 = 22$ cm.

But the diagram shows the stem extending downward from the bottom of the top rectangle.

So yes — two rectangles stacked:

1. Top rectangle: $25 \times 12 = 300\,\text{cm}^2$
2. Stem: $6 \times 10 = 60\,\text{cm}^2$

Total area = $300 + 60 = 360\,\text{cm}^2$

✔ Answer (b): 360 cm²

---

## ✔ (c)

```
4cm
┌──────┐
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
┌──────┼──────┐
│ │ │
│ 3cm │ │
│ │ │
└──────┴──────┘
13cm
```

This is an L-shaped figure.

Break it into two rectangles:

Option 1:
- Top rectangle: width = 4 cm, height = 10 cm → $4 \times 10 = 40\,\text{cm}^2$
- Bottom rectangle: width = 13 cm, height = 3 cm → $13 \times 3 = 39\,\text{cm}^2$

But wait — the top rectangle is only 4 cm wide, and the bottom is 13 cm wide, so the overlap is 4 cm.

The bottom rectangle extends 13 cm, but the top only covers 4 cm, so the bottom rectangle should be 13 cm wide, but only 3 cm high.

But the top rectangle is 4 cm wide, and 10 cm high, and sits on top of the right end of the bottom.

Wait — actually, the total height is 10 cm, and the bottom is 3 cm high, so the top is $10 - 3 = 7$ cm high?

But the label says "10cm" on the side — that's the total height.

And the bottom is labeled 3 cm high.

So:
- The bottom rectangle is 13 cm wide × 3 cm high → $13 \times 3 = 39\,\text{cm}^2$
- The top rectangle is 4 cm wide × $10 - 3 = 7$ cm high → $4 \times 7 = 28\,\text{cm}^2$

Total area = $39 + 28 = 67\,\text{cm}^2$

✔ Answer (c): 67 cm²

---

## ✔ (d)

```
2cm
┌──────┐
│ │
│ 5cm │
│ │
│ │
├──────┼──────┐
│ │ │
│ 4cm │ 3cm │
│ │ │
└──────┴──────┘
9cm
```

This is a T-shape upside-down.

Break into:
- Base rectangle: width = 9 cm, height = 3 cm → $9 \times 3 = 27\,\text{cm}^2$
- Middle rectangle: width = 2 cm, height = 5 cm → $2 \times 5 = 10\,\text{cm}^2$

But wait — the middle rectangle is on top of the base, and the base is 9 cm wide, but the middle is only 2 cm wide.

But the middle is also connected to the left side?

Wait — the left part is 4 cm wide, and the right part is 3 cm wide, and the top is 2 cm wide.

Wait — actually, the horizontal bar is 2 cm wide and 5 cm tall, and it's sitting on top of the base.

But the base is 9 cm wide, and the top bar is only 2 cm wide — where is it placed?

Looking at the diagram:
- The top bar is 2 cm wide and 5 cm tall.
- It's placed such that its bottom edge is aligned with the top of the base.
- The base is 3 cm tall, and 9 cm wide.
- The top bar is centered? Or aligned left?

But the left side of the shape has a 4 cm width, and the right has a 3 cm width, so the top bar must be centered.

But the top bar is 2 cm wide, so it’s small.

So total area:
- Base: $9 \times 3 = 27\,\text{cm}^2$
- Top bar: $2 \times 5 = 10\,\text{cm}^2$

But wait — the top bar is not sitting on the entire base — it's just on top.

But the vertical connection is only 2 cm wide.

But the shape includes:
- A left column: 4 cm wide, total height = 3 + 5 = 8 cm?
- A right column: 3 cm wide, height = 3 cm
- A top bar: 2 cm wide, 5 cm tall, sitting on top of the left?

Wait — no. The top bar is 2 cm wide, and the left is 4 cm wide, so it could be centered.

But the total height of the shape is $3 + 5 = 8$ cm.

But the top bar is 5 cm tall, and the base is 3 cm tall.

But the left side has a 4 cm width, and the right has a 3 cm width, so the base is 9 cm wide.

But the top bar is 2 cm wide — so it's centered?

Yes.

So:
- Base rectangle: $9 \times 3 = 27\,\text{cm}^2$
- Top rectangle: $2 \times 5 = 10\,\text{cm}^2$

But wait — the top bar is on top of the base, so total area = $27 + 10 = 37\,\text{cm}^2$

But is there any overlap? No — it's just added.

But wait — the top bar is not covering the entire base — it's just a small piece on top.

But the left side is 4 cm wide, and the top bar is 2 cm wide — so it might be centered on the left?

But the diagram shows:
- From the left: 4 cm width (left column)
- Then 2 cm width (top bar)
- Then 3 cm width (right column)

Wait — no — the top bar is only 2 cm wide, and it's on top of the left?

But the base is 9 cm wide: 4 cm + ? + 3 cm = 7 cm — missing 2 cm.

Ah! So the top bar is centered above the base, so it’s 2 cm wide, and the base is 9 cm wide.

But the left is 4 cm, right is 3 cm, so the middle is 2 cm — so the top bar is on the middle 2 cm of the base.

So the top bar is 2 cm wide, 5 cm tall, sitting on the middle of the base.

So:
- Base: $9 \times 3 = 27\,\text{cm}^2$
- Top bar: $2 \times 5 = 10\,\text{cm}^2$

Total area = $27 + 10 = 37\,\text{cm}^2$

✔ Answer (d): 37 cm²

---

## ✔ (e)

```
24cm
┌────────────┐
│ │
│ 8cm │
│ │
├─────┬─────┬─────┤
│ │ │ │
│ 6cm │ 6cm │ 2cm │
│ │ │ │
└─────┴─────┴─────┘
20cm
```

This is a rectangle with three rectangular holes cut out at the bottom.

So:
- Large rectangle: $24 \times 20 = 480\,\text{cm}^2$
- Three smaller rectangles removed (cutouts):
- First: $6 \times 8 = 48\,\text{cm}^2$
- Second: $6 \times 8 = 48\,\text{cm}^2$
- Third: $2 \times 8 = 16\,\text{cm}^2$

Total removed area = $48 + 48 + 16 = 112\,\text{cm}^2$

So total area = $480 - 112 = 368\,\text{cm}^2$

✔ Answer (e): 368 cm²

---

## ✔ (f)

```
8cm
┌────────────┐
│ │
│ 7cm │
│ │
├─────┬─────┤
│ │ │
│ 2cm │ 3cm │
│ │ │
└─────┴─────┘
3cm
```

Wait — the bottom is labeled: 2 cm, 3 cm, and the top is 8 cm.

But the total width is 8 cm.

The cutout is 3 cm wide and 3 cm high.

Wait — the height of the cutout is labeled as 3 cm, and the depth is 3 cm?

But the total height is 7 cm, and the cutout is 3 cm high.

So:
- Large rectangle: $8 \times 7 = 56\,\text{cm}^2$
- Cutout: $3 \times 3 = 9\,\text{cm}^2$

So area = $56 - 9 = 47\,\text{cm}^2$

Wait — but the cutout is 3 cm wide, and the gap is 3 cm high.

But the label says:
- Bottom: 2 cm, then 3 cm (cutout), then nothing — but total width is 8 cm.

Wait — the cutout is 3 cm wide, and the remaining parts are 2 cm and 3 cm?

Wait — the bottom has:
- Left: 2 cm
- Middle: 3 cm (cutout)
- Right: 3 cm?

But 2 + 3 + 3 = 8 cm — yes.

But the cutout is 3 cm wide and 3 cm high, and it's in the center.

So yes:
- Large rectangle: $8 \times 7 = 56\,\text{cm}^2$
- Cutout: $3 \times 3 = 9\,\text{cm}^2$

Total area = $56 - 9 = 47\,\text{cm}^2$

✔ Answer (f): 47 cm²

---

## ✔ Final Answers:

| Shape | Area |
|-------|------|
| (a) | 62 cm² |
| (b) | 360 cm² |
| (c) | 67 cm² |
| (d) | 37 cm² |
| (e) | 368 cm² |
| (f) | 47 cm² |

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Let me know if you'd like diagrams or step-by-step breakdowns for any specific one!