This worksheet helps students practice finding the area of complex L-shaped and stepped polygons by breaking them down into simpler rectangles.

Let's solve each of these rectilinear shapes by dividing them into rectangles and calculating their areas. We'll go step-by-step.

---

1) First Shape

Given:
- Top rectangle: width = 8 cm, height = 3 cm
- Bottom rectangle: width = 5 cm, height = (10 - 3) = 7 cm

We can split this shape into two rectangles:
- Top rectangle: 8 cm × 3 cm
- Bottom rectangle: 5 cm × 7 cm

Now calculate the area:

- Area of top rectangle = $ 8 \times 3 = 24 \text{ cm}^2 $
- Area of bottom rectangle = $ 5 \times 7 = 35 \text{ cm}^2 $

Total Area = 24 + 35 = 59 cm²

✔ Answer: 59 cm²

---

2) Second Shape

This shape has a "bite" taken out from the right side.

We can divide it into two rectangles:
- Left rectangle: 6 cm wide, 7 cm tall
- Right rectangle: (10 - 6) = 4 cm wide, 5 cm tall

Wait — let’s look carefully.

Actually, the total height is 7 cm on the left, but only 5 cm on the right. So we can split it vertically:

- Left rectangle: 6 cm × 7 cm
- Right rectangle: (10 - 6) = 4 cm × 5 cm

But wait — the top part is 10 cm long, and the bottom part is 6 cm long. The missing piece is on the lower right.

So better to think:
- The full rectangle would be 10 cm × 7 cm = 70 cm²
- But there's a missing rectangle of size: (10 - 6) = 4 cm wide, and (7 - 5) = 2 cm high → so 4 × 2 = 8 cm² missing?

No — actually, the bottom-right portion is missing.

Wait — let's re-analyze.

Looking at the figure:
- Total height on left = 7 cm
- Right side drops to 5 cm
- Bottom base is 6 cm
- Top is 10 cm

So we can split it into:
1. A left rectangle: 6 cm (width) × 7 cm (height)
2. A right rectangle: (10 - 6) = 4 cm (width), but height is only 5 cm

So:
- Left: $ 6 \times 7 = 42 \text{ cm}^2 $
- Right: $ 4 \times 5 = 20 \text{ cm}^2 $

Total Area = 42 + 20 = 62 cm²

✔ Answer: 62 cm²

---

3) Third Shape

Dimensions:
- Top rectangle: 30 mm × 5 mm
- Bottom rectangle: 20 mm × 7 mm

But note: the bottom rectangle sticks out on the right, and the top one is wider.

Wait — actually, the total length is 30 mm, and the bottom section is 20 mm, so the left part is 30 - 20 = 10 mm wide? Let's visualize.

The shape looks like an "L" turned sideways.

We can split it into:
- Top rectangle: 30 mm (length) × 5 mm (height)
- Bottom rectangle: 20 mm (length) × 7 mm (height)

But they overlap in the middle? No — actually, the bottom rectangle sits below the top one, but only extends 20 mm to the right.

Wait — better to think:

- The left part is a rectangle: 10 mm wide (30 - 20) and (5 + 7) = 12 mm tall?
No — that's not correct.

Let’s label it clearly.

From the diagram:
- The top horizontal segment is 30 mm long and 5 mm high.
- Below it, a vertical drop of 7 mm, but only over a width of 20 mm.
- So the bottom rectangle is 20 mm wide and 7 mm tall.
- The top rectangle is 30 mm wide and 5 mm tall.

But they are adjacent — the top rectangle covers the full width, and the bottom one is only 20 mm wide.

So we can split it into:
1. Top rectangle: 30 mm × 5 mm = 150 mm²
2. Bottom rectangle: 20 mm × 7 mm = 140 mm²

Are they overlapping? No — they're stacked vertically, but the bottom one is narrower.

Wait — no! Actually, the top rectangle is on top, and the bottom rectangle is attached to the right side of the top one? Or is it aligned?

Looking at the image:
- The top rectangle is 30 mm long and 5 mm high.
- Then below it, there's a rectangle that is 20 mm wide and 7 mm high, but it starts from the right end of the top rectangle?

No — actually, the bottom rectangle is underneath the top one, but only extending 20 mm to the right.

So the left 10 mm of the bottom part is missing?

Wait — perhaps the shape is like a large rectangle with a smaller rectangle sticking out.

Actually, looking at the dimensions:
- The total height on the right side is 5 mm (top) + 7 mm (bottom) = 12 mm
- The total width is 30 mm
- But the bottom rectangle is only 20 mm wide

So the shape consists of:
- A large rectangle on the left: 10 mm wide (30 - 20), and 12 mm high (5 + 7)
- A smaller rectangle on the right: 20 mm wide, 5 mm high (top), plus 20 mm × 7 mm (bottom)? No — that doesn't work.

Better idea: split into two parts:

Option: Divide the shape into:
1. Top rectangle: 30 mm × 5 mm = 150 mm²
2. Bottom rectangle: 20 mm × 7 mm = 140 mm²

But do they overlap? Yes — if both are placed such that the bottom one is under the top one, then the overlapping region is 20 mm × 5 mm? But that would mean double-counting.

Wait — no. The bottom rectangle is attached to the bottom of the top one, but only for 20 mm.

So the total shape is:
- A rectangle of 30 mm × 5 mm (top)
- Plus a rectangle of 20 mm × 7 mm (bottom), but only on the right side.

But the bottom rectangle should extend below the top one, and its width is 20 mm.

So the left 10 mm of the bottom part is not covered — meaning the shape has a step.

Wait — actually, the bottom rectangle is entirely below the top one, and is 20 mm wide, so the left 10 mm of the full width has only the top rectangle (5 mm high), and the right 20 mm has both top and bottom.

But the bottom rectangle is 7 mm high, so total height on the right is 5 + 7 = 12 mm.

So the shape is:
- Left part: 10 mm wide × 5 mm high (only top)
- Right part: 20 mm wide × (5 + 7) = 12 mm high

But that’s not accurate — because the bottom rectangle is only 7 mm high, and it's attached below the top rectangle.

So total area = area of top rectangle + area of bottom rectangle

- Top: 30 mm × 5 mm = 150 mm²
- Bottom: 20 mm × 7 mm = 140 mm²

But are they overlapping? Only if the bottom rectangle overlaps the top one.

But since the bottom rectangle is under the top one, and both have same width? No — the bottom one is only 20 mm wide, while the top is 30 mm.

So the bottom rectangle is aligned to the right under the top one.

So the overlap is 20 mm × 5 mm? But that’s not how area works — you don’t subtract.

Actually, no overlap — they are adjacent vertically, but the bottom one is only 20 mm wide, so it sits under the right 20 mm of the top rectangle.

So the total area is:
- Top: 30 × 5 = 150 mm²
- Bottom: 20 × 7 = 140 mm²

And since they are adjacent, no overlap — total area = 150 + 140 = 290 mm²

But wait — is the bottom rectangle sitting directly below the top one? If so, then the left 10 mm of the bottom part is missing — but the shape is continuous.

Wait — maybe the bottom rectangle is attached to the right side of the top one?

No — the diagram shows the bottom rectangle is underneath the top one, but only covering the right 20 mm.

So the total shape has:
- A vertical strip on the left: 10 mm wide, 5 mm high
- A larger rectangle on the right: 20 mm wide, 12 mm high (5 + 7)

That makes more sense.

So:
- Left rectangle: 10 mm × 5 mm = 50 mm²
- Right rectangle: 20 mm × 12 mm = 240 mm²

Total area = 50 + 240 = 290 mm²

Same as before.

✔ Answer: 290 mm²

---

4) Fourth Shape

Units: meters

Dimensions:
- Top: 7½ m wide, 4 m high
- Bottom: 1½ m wide, 2 m high

But the bottom rectangle is attached to the right of the top one?

Wait — looking at the shape:
- The top rectangle is 7½ m wide and 4 m high
- Then a step down to a smaller rectangle on the right: 1½ m wide and 2 m high

But the total height on the right is 4 + 2 = 6 m? No — the bottom rectangle is below the top one.

Wait — the bottom rectangle is shorter and narrower, and sits under the top one, but only on the right side.

But the top rectangle is 7½ m wide, and the bottom rectangle is 1½ m wide, and it’s attached to the right side of the top one?

No — the diagram shows:
- The top rectangle is 7½ m wide and 4 m high
- Then a drop of 1½ m, and a bottom rectangle of 1½ m wide and 2 m high

Wait — the heights:
- The top rectangle is 4 m high
- Then a gap of 1½ m? No — the bottom rectangle is 2 m high, and the total height is 4 + 2 = 6 m?

But the bottom rectangle is only 1½ m wide.

Wait — actually, the bottom rectangle is attached to the right side of the top one, but lowered.

But the top rectangle is 7½ m wide, and the bottom rectangle is 1½ m wide and 2 m high.

But the total height of the shape is 4 m (top) + 2 m (bottom) = 6 m?

No — the bottom rectangle is below the top one, but only on the right.

So the total shape consists of:
- A large rectangle: 7½ m × 4 m (top)
- A small rectangle: 1½ m × 2 m (bottom), attached to the right of the top one, but lower?

Wait — the bottom rectangle is not aligned — it's indented.

Actually, the bottom rectangle is under the top one, but only on the right side, and it's shorter.

But the total width is 7½ m, and the bottom rectangle is 1½ m wide.

So the bottom rectangle is attached to the right side of the top one, but downward.

But the top rectangle is 7½ m wide, and the bottom rectangle is 1½ m wide — so it’s not aligned.

Wait — better to split into:
1. Top rectangle: 7½ m × 4 m
2. Bottom rectangle: 1½ m × 2 m

But are they connected? Yes — the bottom rectangle is attached to the bottom-right corner of the top one.

But the total area is just the sum.

But is there any overlap? No — they are adjacent.

But the bottom rectangle is only 1½ m wide, and the top rectangle is 7½ m wide.

So the total shape has:
- A large rectangle on the top: 7½ m × 4 m
- A small rectangle on the bottom right: 1½ m × 2 m

But the bottom rectangle is not under the entire width — only under the right 1½ m.

So the area is:
- Top: $ 7.5 \times 4 = 30 \text{ m}^2 $
- Bottom: $ 1.5 \times 2 = 3 \text{ m}^2 $

Total area = 30 + 3 = 33 m²

But wait — is the bottom rectangle attached to the bottom of the top one? Or is it offset?

Looking at the diagram:
- The top rectangle is 7½ m wide and 4 m high
- Then a step down of 1½ m, and a bottom rectangle of 1½ m wide and 2 m high

Wait — the height of the bottom rectangle is 2 m, and it's below the top one.

But the top rectangle is 4 m high, and the bottom rectangle is 2 m high, so the total height is 4 + 2 = 6 m?

But the bottom rectangle is only 1½ m wide.

So the shape is:
- A large rectangle of 7½ m × 4 m (top)
- A small rectangle of 1½ m × 2 m (bottom), attached to the right edge of the top one, but lower.

But that would make the bottom rectangle protrude to the right.

But the bottom rectangle is only 1½ m wide, so it's not extending beyond.

Wait — perhaps the bottom rectangle is under the top one, but only on the right side.

So the total area is:
- Top: 7.5 × 4 = 30 m²
- Bottom: 1.5 × 2 = 3 m²

Total = 33 m²

But is there a gap? No — the bottom rectangle is attached.

But the bottom rectangle is only 1.5 m wide, so it’s not filling the whole width.

So yes, the total area is simply the sum.

Alternatively, think of it as:
- The top rectangle: 7.5 × 4 = 30
- The bottom rectangle: 1.5 × 2 = 3

No overlap.

✔ Answer: 33 m²

---

✔ Final Answers:

1) 59 cm²
2) 62 cm²
3) 290 mm²
4) 33 m²

---

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