Math worksheet for calculating the area of rectilinear shapes by dividing them into rectangles.

Let's solve each of these rectilinear shapes by dividing them into rectangles and calculating the total area. We'll go step-by-step for each shape.

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1) Shape 1

Given:
- Top rectangle: width = 8 cm, height = 2½ cm
- Bottom rectangle: width = 3 cm, height = (6 - 2½) = 3.5 cm

But wait — let’s look carefully:

The full height on the right is 6 cm, and the top part is 2½ cm high. So the bottom rectangle has a height of:
> 6 cm − 2½ cm = 3.5 cm

Now, we need to find the widths.

- The top rectangle: width = 8 cm, height = 2.5 cm
- The bottom rectangle: width = 3 cm, height = 3.5 cm

Wait — but the bottom part extends only 3 cm in width, so it must be aligned with the right side. That means the left portion of the bottom rectangle must be missing? Let’s think differently.

Actually, this shape is like an "L" rotated. It's better to split it into two rectangles:

#### Option: Split vertically or horizontally?

We can split it into two rectangles:

- Rectangle A: Top left — 8 cm wide × 2.5 cm high
- Rectangle B: Bottom right — 3 cm wide × (6 − 2.5) = 3.5 cm high

But wait — does that cover the whole shape?

Yes! The bottom rectangle is 3 cm wide and 3.5 cm tall, sitting at the bottom right.

So:
- Area of A = 8 × 2.5 = 20 cm²
- Area of B = 3 × 3.5 = 10.5 cm²

Total area = 20 + 10.5 = 30.5 cm²

✔ Answer: 30.5 cm²

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2) Shape 2

This is another L-shaped figure.

Dimensions:
- Left vertical rectangle: 6 mm wide, 20 mm high
- Right horizontal rectangle: 10 mm wide, 15 mm high

But note: the total height is 20 mm, and the right piece is 15 mm high, so the overlap is 15 mm.

So:
- Rectangle A (left): 6 mm × 20 mm = 120 mm²
- Rectangle B (right): 10 mm × 15 mm = 150 mm²

But wait — if we add these, we’re double-counting the overlapping region? No — actually, the two rectangles are adjacent, not overlapping.

Let’s check: the left rectangle goes full height (20 mm), width 6 mm. The right one is attached to the right side, but only 15 mm tall, so it starts from the bottom.

So the total shape is made of:
- A vertical rectangle on the left: 6 mm × 20 mm
- A horizontal rectangle on the right: 10 mm × 15 mm

But now, do they overlap? Only where both exist — yes, the bottom 15 mm of the left rectangle overlaps with the right one? No — actually, the right rectangle is attached to the right edge of the left one, but only 15 mm tall.

So the total area is just:
- Left rectangle: 6 mm × 20 mm = 120 mm²
- Right rectangle: 10 mm × 15 mm = 150 mm²

But wait — the right rectangle is not sitting on top of the left one; it’s attached to the right side of the bottom 15 mm of the left rectangle.

So the overlapping region is not in area — they're adjacent, no overlap.

But actually, the left rectangle is 6 mm wide × 20 mm tall → covers the full left side.

The right rectangle is 10 mm wide × 15 mm tall, starting from the bottom.

So the combined shape is:
- Left column: 6 mm × 20 mm
- Right extension: 10 mm × 15 mm

But the right extension is attached to the bottom 15 mm of the left column — so the total area is:

> Area = (6 × 20) + (10 × 15) = 120 + 150 = 270 mm²

But wait — is there overlap? No — the right rectangle is to the right of the left one, and only extends up 15 mm. The left one is 20 mm tall, so the top 5 mm of the left rectangle is alone.

So yes, no overlap, just adjacent.

✔ Answer: 270 mm²

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3) Shape 3

This is a rectangle with a corner cut out.

Dimensions:
- Outer rectangle: 8 cm wide, 5 cm high
- Cut-out: a small rectangle removed from the top-right corner

The cut-out is:
- Width = (8 - 5) = 3 cm
- Height = 1½ cm

So:
- Area of full rectangle = 8 × 5 = 40 cm²
- Area of cut-out = 3 × 1.5 = 4.5 cm²
- Total area = 40 - 4.5 = 35.5 cm²

Alternatively, divide into two rectangles:

- Left rectangle: 5 cm × 5 cm = 25 cm²
- Right rectangle: (8 - 5) = 3 cm wide, but height = (5 - 1.5) = 3.5 cm → 3 × 3.5 = 10.5 cm²

Wait — that gives 25 + 10.5 = 35.5 cm² → same answer.

✔ Answer: 35.5 cm²

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4) Shape 4

Another L-shape.

Dimensions:
- Left rectangle: 1.5 m wide, 5 m high
- Right rectangle: 3.5 m wide, 2 m high

Note: The right rectangle is attached to the bottom of the left one.

So:
- Rectangle A (left): 1.5 m × 5 m = 7.5 m²
- Rectangle B (right): 3.5 m × 2 m = 7 m²

Are they adjacent? Yes — the right rectangle sits to the right of the bottom 2 m of the left rectangle.

No overlap, so total area = 7.5 + 7 = 14.5 m²

✔ Answer: 14.5 m²

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✔ Final Answers:

1) 30.5 cm²
2) 270 mm²
3) 35.5 cm²
4) 14.5 m²

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🔍 Summary of Methods:

- For compound shapes, divide into rectangles.
- Use addition if separate rectangles.
- Use subtraction if a rectangle is missing (cut-out).
- Always check units and ensure correct dimensions.

Let me know if you want diagrams or visual breakdowns!