Worksheet with compound shapes to calculate area, including dimensions and a video link for guidance.

Let's solve Question 1 from the image:
Work out the area of each of these compound shapes.

We'll break each shape into simpler rectangles, calculate their areas, and sum them up.

---

(a)

This shape can be split into two rectangles:

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

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

> Note: The bottom part is only 7 cm wide (as shown), and it’s sitting below the top part.

But wait — actually, we need to check if this is correct. The total width at the base is 7 cm, but the top is 9 cm. So the bottom rectangle is only 7 cm wide, and the top extends 1 cm on each side? Wait — no.

Looking closely:
- The top rectangle is 9 cm wide and 8 cm tall.
- The bottom rectangle is 7 cm wide and 5 cm tall, but it’s attached to the right side of the top one?

Wait — actually, let's re-analyze.

From the diagram:
- The full vertical height is 8 cm + 5 cm = 13 cm?
- But the left side has a step down.

Actually, the shape is like a "staircase" or L-shape.

Better approach: Split into two rectangles.

Let’s divide the shape vertically:
- Left rectangle: width = 5 cm, height = 8 cm → area = $ 5 \times 8 = 40 $
- Right rectangle: width = 7 cm, height = 5 cm → area = $ 7 \times 5 = 35 $

But wait — the total width is 9 cm, and the right part is 7 cm wide, so the left part must be 9 - 7 = 2 cm? That doesn't match the 5 cm label.

Wait — look again.

The horizontal dimension at the top is 9 cm.
At the bottom, it's 7 cm.
The vertical drop is 5 cm.

So, the shape has:
- A top rectangle: 9 cm × 8 cm → area = $ 9 \times 8 = 72 $
- A bottom rectangle: 7 cm × 5 cm → area = $ 7 \times 5 = 35 $

But are they overlapping? No — the bottom rectangle sits under the right part of the top one.

So, total area = $ 72 + 35 = 107 \text{ cm}^2 $

Wait — but is that correct?

Let’s double-check:

The left side of the shape goes down 8 cm, then continues horizontally for 5 cm? No.

Actually, from the diagram:
- The total height is 8 cm (top) and then an extra 5 cm below? No — the 5 cm is the height of the lower section.

Wait — looking carefully:

The vertical side on the left is 8 cm high, then drops down 5 cm? No — the label 5cm is the height of the bottom rectangle.

So:
- Top rectangle: 9 cm (width) × 8 cm (height) → $ 9 \times 8 = 72 $
- Bottom rectangle: 7 cm (width) × 5 cm (height) → $ 7 \times 5 = 35 $

But the bottom rectangle is only 7 cm wide, and the top is 9 cm wide — so the bottom rectangle is centered? Or offset?

From the diagram:
- The bottom rectangle starts where the top rectangle ends on the left? No — the step is on the right.

Actually, the top rectangle is 9 cm wide and 8 cm tall.
Then, the bottom rectangle is 7 cm wide and 5 cm tall, and it’s attached to the bottom-left of the top rectangle?

No — the gap between the top and bottom parts is on the right.

Wait — better: imagine splitting the shape into two rectangles:

1. Left rectangle: width = 5 cm (from the left edge), height = 8 + 5 = 13 cm? No — the 5 cm is the height of the lower part.

Wait — here’s the key: the vertical line on the left is 8 cm tall, then the bottom extends another 5 cm, but only for 7 cm in width.

So the total shape can be split as:

- Rectangle A: 5 cm (width) × 13 cm (height)? No — the 5 cm is horizontal.

Let me redraw mentally.

From the diagram:
- The top part is 9 cm wide and 8 cm tall.
- Then, below it, there’s a lower part that is 7 cm wide and 5 cm tall.
- But the left edge of the lower part aligns with the left edge of the top part? No — the lower part is shorter.

Actually, the step is on the right.

So the top rectangle is 9 cm wide, 8 cm tall.

The bottom rectangle is 7 cm wide, 5 cm tall, and its left edge is aligned with the left edge of the top rectangle.

But the top rectangle extends 9 cm, while the bottom only 7 cm — so the bottom rectangle is under the first 7 cm of the top rectangle.

So the overlapping region is 7 cm × 8 cm? No — the bottom rectangle is only 5 cm tall.

So the area is:
- Top rectangle: 9 × 8 = 72
- Bottom rectangle: 7 × 5 = 35
- But they overlap? Only in the 7 cm width and 5 cm height — but since the bottom rectangle is below the top, and the top is 8 cm tall, the bottom rectangle is below the top, so no overlap.

Wait — the height of the top rectangle is 8 cm, and the bottom is 5 cm tall — so the total height is 8 + 5 = 13 cm? But the bottom rectangle is attached to the bottom of the top rectangle?

No — the diagram shows a step on the right side.

Let’s interpret:

- The top part is 9 cm wide, 8 cm tall.
- The bottom part is 7 cm wide, 5 cm tall, and it’s shifted to the right by 2 cm?

Wait — the bottom width is 7 cm, and the top is 9 cm, so the bottom is 2 cm shorter on the right.

But the bottom rectangle is attached to the left of the top?

Wait — the vertical line on the left is 8 cm tall, then goes down 5 cm — so the left side is continuous.

The right side has a step: the top is 9 cm wide, then the bottom is only 7 cm wide, so it steps inward by 2 cm.

So the shape is:

- Left side: full height = 8 + 5 = 13 cm
- Right side: top 8 cm, then steps in to 7 cm width, then 5 cm down.

So we can split into:

1. Left rectangle: width = 5 cm (since bottom is 7 cm wide, and top is 9 cm, difference is 2 cm on each side? Wait — no)

Wait — the bottom part is 7 cm wide, and the top is 9 cm wide, so the step is 2 cm inward on the right.

But the left edge is straight.

So the shape can be divided into:

- Rectangle 1: width = 7 cm, height = 8 + 5 = 13 cm → area = $ 7 \times 13 = 91 $
- Rectangle 2: width = 2 cm, height = 8 cm (the overhang on the top) → area = $ 2 \times 8 = 16 $

Total area = $ 91 + 16 = 107 \text{ cm}^2 $

Yes! This makes sense.

Alternatively:
- Top rectangle: 9 × 8 = 72
- Bottom rectangle: 7 × 5 = 35
- Total = 72 + 35 = 107 cm²

Same answer.

✔ Answer (a): 107 cm²

---

(b)

T-shaped figure.

Split into two rectangles:

- Top rectangle: 25 cm × 12 cm → area = $ 25 \times 12 = 300 $
- Bottom rectangle: 6 cm × (12 - 10) = 6 cm × 2 cm = 12 cm²? No.

Wait — the height of the stem is 10 cm, and the top is 12 cm high, so the stem is 10 cm tall.

But the total height is 12 cm, and the stem is 10 cm tall, so the top is 2 cm thick? No — the top is 12 cm tall, and the stem is 10 cm tall — but the stem is below the top.

Wait — the total height is 12 cm, and the stem is 10 cm tall, so the top is 2 cm thick? No — the top is the upper part.

Wait — the label says:
- Total height: 12 cm
- Stem height: 10 cm
- So the top is 12 - 10 = 2 cm tall? But the top is wide.

Wait — no: the top is 25 cm wide, and the stem is 6 cm wide.

And the height of the top is not labeled — but the total height is 12 cm, and the stem is 10 cm tall, so the top must be 2 cm tall.

Yes!

So:
- Top rectangle: 25 cm × 2 cm = 50 cm²
- Stem rectangle: 6 cm × 10 cm = 60 cm²

Total area = $ 50 + 60 = 110 \text{ cm}^2 $

✔ Answer (b): 110 cm²

---

(c)

L-shaped figure.

Split into two rectangles:

- Top rectangle: 4 cm × 10 cm = 40 cm²
- Bottom rectangle: 13 cm × 3 cm = 39 cm²

But do they overlap? No — the top rectangle is on the right, bottom on the left.

Wait — the total width is 13 cm, and the top rectangle is 4 cm wide, so the bottom rectangle must be 13 cm wide, but the top is only 4 cm wide.

So the bottom rectangle is 13 cm × 3 cm = 39 cm²

The top rectangle is 4 cm wide, and its height is 10 cm, but the bottom part is only 3 cm tall, so the top rectangle is 10 - 3 = 7 cm tall?

Wait — the total height is 10 cm, and the bottom is 3 cm tall, so the top is 7 cm tall.

But the label says the top rectangle is 4 cm wide, and the total height is 10 cm, and the bottom is 3 cm tall, so the top is 7 cm tall.

So:
- Top rectangle: 4 cm × 7 cm = 28 cm²
- Bottom rectangle: 13 cm × 3 cm = 39 cm²

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

✔ Answer (c): 67 cm²

---

(d)

Shape with a "step" upward.

Split into three rectangles? Or two.

Better: split into:
- Bottom rectangle: 9 cm × 3 cm = 27 cm²
- Middle rectangle: 4 cm × 5 cm = 20 cm²
- Top rectangle: 2 cm × 5 cm = 10 cm²

But wait — the middle and top are stacked.

Wait — the bottom is 9 cm wide, 3 cm tall.

Above it, on the left, a rectangle 4 cm wide, 5 cm tall.

On the right, a rectangle 2 cm wide, 5 cm tall.

But the total width is 9 cm.

So:
- Bottom: 9 × 3 = 27
- Middle-left: 4 × 5 = 20
- Top-right: 2 × 5 = 10

But the middle-left is 4 cm wide, and the top-right is 2 cm wide — total width = 4 + 2 = 6 cm, but the bottom is 9 cm — so there’s a gap?

Wait — no: the bottom is 9 cm wide.

Then, above it, on the left, a 4 cm wide rectangle (5 cm tall), and on the right, a 2 cm wide rectangle (5 cm tall). But that’s only 6 cm total width.

But the total width is 9 cm — so the middle must extend across.

Wait — the diagram shows:
- Bottom: 9 cm wide, 3 cm tall
- Above it, a rectangle 4 cm wide (on the left), 5 cm tall
- Then, above that, a smaller rectangle 2 cm wide, 5 cm tall — but that would be offset.

Wait — actually, the top is only 2 cm wide, and it’s on the right.

So the shape is:
- Bottom: 9 cm × 3 cm = 27
- Middle: 4 cm × 5 cm = 20 (on the left)
- Top: 2 cm × 5 cm = 10 (on the right, but above the middle?)

No — the top is 2 cm wide, and it’s on the right, but it’s not directly above the bottom.

Wait — the label says:
- Bottom: 9 cm wide
- Then, a step up on the left: 4 cm wide, 5 cm tall
- Then, on the right, a 2 cm wide rectangle, 5 cm tall — but it’s above the bottom?

Wait — the total height is 3 + 5 = 8 cm? But the top is 5 cm tall.

Actually, the bottom is 3 cm tall, and above it, there’s a structure that is 5 cm tall.

But the width varies.

Best to split into:

1. Bottom rectangle: 9 cm × 3 cm = 27 cm²
2. Left middle rectangle: 4 cm × 5 cm = 20 cm²
3. Right top rectangle: 2 cm × 5 cm = 10 cm²

But the right top is 2 cm wide, and it’s on the right, but how does it connect?

Wait — the total width at the top is 2 cm, and at the bottom is 9 cm.

But the left part has a 4 cm wide extension upward.

So the right part must be narrower.

But the right top is 2 cm wide, and it’s above the bottom.

But the bottom is 9 cm wide, so the right top is only 2 cm wide — so it must be offset.

But the total width is 9 cm.

Wait — the diagram shows:
- Bottom: 9 cm wide
- On the left, a step up of 4 cm wide, 5 cm tall
- On the right, a smaller rectangle 2 cm wide, 5 cm tall — but it’s above the bottom?

But the bottom is 9 cm wide, so the right top must be within the 9 cm.

But the total width at the top is only 2 cm? That doesn’t make sense.

Wait — the label says:
- Bottom: 9 cm
- Then, a step on the left: 4 cm wide, 5 cm tall
- Then, a top rectangle: 2 cm wide, 5 cm tall — but it’s on the right, so the middle is missing.

Wait — perhaps the shape is:

- Bottom: 9 cm × 3 cm = 27
- Then, a rectangle 4 cm wide, 5 cm tall, on the left
- And a rectangle 2 cm wide, 5 cm tall, on the right
- But the gap between them is 9 - 4 - 2 = 3 cm — so the middle is not filled.

But the diagram shows a solid shape — so the top must be connected.

Wait — perhaps the top is only 2 cm wide, and it’s on the right, and the left has a 4 cm wide rectangle extending up.

But the bottom is 9 cm wide, so the top is narrower.

So the area is:

- Bottom: 9 × 3 = 27
- Left column: 4 × 5 = 20
- Right column: 2 × 5 = 10

But the left column is 4 cm wide, and the right column is 2 cm wide — total width = 6 cm, but the bottom is 9 cm — so there’s a gap of 3 cm in the middle?

But the diagram shows a solid shape — so likely, the top is only 2 cm wide, and it’s on the right, and the left has a 4 cm wide extension, but the middle is not filled.

But that would leave a gap.

Wait — perhaps the top is 2 cm wide, and it’s on the right, and the left has a 4 cm wide extension, and the middle is filled with the bottom.

But the bottom is 9 cm wide, so the entire bottom is filled.

Then, above the left 4 cm, there is a 5 cm tall rectangle.

Above the right 2 cm, there is a 5 cm tall rectangle.

But what about the middle 3 cm (9 - 4 - 2 = 3 cm)? It’s only 3 cm wide, and it’s not extended — so the top is only 4 + 2 = 6 cm wide?

But the diagram shows the top is only 2 cm wide.

Wait — I think I'm misreading.

Look at the labels:

- The bottom is 9 cm wide
- The left step is 4 cm wide, 5 cm tall
- The top is 2 cm wide, 5 cm tall — and it’s on the right, so it must be above the bottom, but only 2 cm wide.

So the shape has:
- Bottom: 9 cm × 3 cm = 27
- Left extension: 4 cm × 5 cm = 20
- Right extension: 2 cm × 5 cm = 10

But the left extension is on the left, the right extension is on the right, and the middle is only 3 cm wide and only 3 cm tall.

So the total area is:
- Bottom: 9 × 3 = 27
- Left top: 4 × 5 = 20
- Right top: 2 × 5 = 10

But the left top is 4 cm wide, 5 cm tall — so it covers from x=0 to x=4, y=3 to y=8
- The right top is 2 cm wide, 5 cm tall — from x=7 to x=9, y=3 to y=8? But 9 - 2 = 7, so x=7 to x=9

But the bottom is from x=0 to x=9, y=0 to y=3

So the left top is from x=0 to x=4, y=3 to y=8
- The right top is from x=7 to x=9, y=3 to y=8

But between x=4 and x=7, there is no shape above y=3 — so it's a gap.

But the diagram shows a solid shape — so this can't be.

Wait — perhaps the top is only 2 cm wide, and it’s on the right, and the left has a 4 cm wide extension, but the middle is filled.

But the labels say:
- The top is 2 cm wide
- The bottom is 9 cm wide
- The left has a 4 cm wide extension upward

But the right has a 2 cm wide extension upward.

So the total width at the top is 4 + 2 = 6 cm? But the label says the top is 2 cm wide — so likely, the top is only 2 cm wide, and it’s on the right.

So the shape is:
- Bottom: 9 × 3 = 27
- Left column: 4 × 5 = 20 (from x=0 to x=4, y=3 to y=8)
- Right column: 2 × 5 = 10 (from x=7 to x=9, y=3 to y=8)

But between x=4 and x=7, there is no fill — so the area is only the bottom and the two columns.

But that leaves a gap — unless the top is only 2 cm wide, and the left is 4 cm wide, and the middle is not filled.

But the diagram shows a solid shape — so likely, the top is 2 cm wide, and it’s on the right, and the left has a 4 cm wide extension, and the middle is filled with the bottom.

But the bottom is 9 cm wide, so the middle is filled.

So the area is:
- Bottom: 9 × 3 = 27
- Left extension: 4 × 5 = 20
- Right extension: 2 × 5 = 10

Total = 27 + 20 + 10 = 57 cm²

But the middle (x=4 to x=7) is only 3 cm wide and 3 cm tall — already included in the bottom.

So yes, the area is 27 + 20 + 10 = 57 cm²

But is the right extension really 2 cm wide? Yes.

And the left extension is 4 cm wide.

And the bottom is 9 cm wide.

So total area = 27 + 20 + 10 = 57 cm²

✔ Answer (d): 57 cm²

---

(e)

Large rectangle with two cutouts.

Outer rectangle: 24 cm × 20 cm = 480 cm²

Cutouts: two identical rectangles, each 6 cm wide, 8 cm tall

Wait — the cutouts are 6 cm wide, and the depth is 8 cm, but the height of the cutout is 8 cm, and the outer height is 20 cm, so the cutouts are 8 cm deep.

Each cutout: 6 × 8 = 48 cm²

Two cutouts: 2 × 48 = 96 cm²

But wait — the third cutout? The diagram shows three cutouts?

Wait — the bottom has three sections: 6 cm, 6 cm, 2 cm — total = 14 cm, but the total width is 24 cm.

So the cutouts are:
- First: 6 cm wide, 8 cm tall
- Second: 6 cm wide, 8 cm tall
- Third: 2 cm wide, 8 cm tall

Wait — the labels show:
- Widths: 6, 6, 2 cm
- Heights: all 8 cm

So the cutouts are:
- 6 × 8 = 48
- 6 × 8 = 48
- 2 × 8 = 16

Total cutout area = 48 + 48 + 16 = 112 cm²

Outer area = 24 × 20 = 480 cm²

So area of shape = 480 - 112 = 368 cm²

✔ Answer (e): 368 cm²

---

(f)

Rectangle with a rectangular hole.

Outer rectangle: 8 cm × 7 cm = 56 cm²

Hole: 3 cm wide, 3 cm tall

Area of hole = 3 × 3 = 9 cm²

But is it fully inside? Yes.

So area = 56 - 9 = 47 cm²

Wait — the hole is 3 cm wide, and the width of the outer rectangle is 8 cm, and the bottom has 2 cm, 3 cm, so the hole is 3 cm wide, and the height is 3 cm.

Yes.

So area = 56 - 9 = 47 cm²

✔ Answer (f): 47 cm²

---

✔ Final Answers:

(a) 107 cm²
(b) 110 cm²
(c) 67 cm²
(d) 57 cm²
(e) 368 cm²
(f) 47 cm²

Let me know if you'd like diagrams or further explanation!