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

You're given a worksheet on finding the area of rectilinear shapes — that is, shapes made up of rectangles joined together. The method is to split the shape into two (or more) rectangles, find the area of each using `Area = length × width`, and then add them together.

Let’s solve each problem step by step.

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Problem 1)

Shape: L-shaped with dimensions:

- Left vertical part: height = 2 cm, width = 1 cm
- Top horizontal part: width = 3 cm, height = 1 cm (since total height is 3 cm, and bottom part is 2 cm)

✔ Split it into two rectangles:

- Rectangle A (bottom left): 2 cm (height) × 1 cm (width) → Area = 2 × 1 = 2 cm²
- Rectangle B (top right): 1 cm (height) × 3 cm (width) → Area = 1 × 3 = 3 cm²

> *Note: You could also split it as a 3×3 square minus a 2×2 square, but the worksheet wants you to add two rectangles.*

✔ Total Area = 2 + 3 = 5 cm²

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Problem 2)

Shape: Looks like a rectangle with a corner cut out — or an “L” rotated.

Dimensions:

- Overall height: 6 cm
- Overall width: 4 cm
- Cut-out: 2 cm wide, 4 cm tall? Wait — let’s interpret correctly.

Actually, from the diagram:

- Left side is 6 cm tall.
- Bottom is 4 cm wide.
- Right side has a step: top part is 4 cm tall, bottom part is 2 cm tall? That doesn’t make sense.

Wait — better way:

✔ Split into two rectangles:

- Rectangle A (left full height): 6 cm (height) × 2 cm (width) → Area = 6 × 2 = 12 cm²
- Rectangle B (top right): 4 cm (height) × 2 cm (width) → Area = 4 × 2 = 8 cm²

> Why? Because the total width is 4 cm. If the left rectangle is 2 cm wide, the right one must be 2 cm wide too. The right rectangle only goes up 4 cm (not 6 cm), so its height is 4 cm.

✔ Total Area = 12 + 8 = 20 cm²

*(Alternative: You could think of the whole 6×4 rectangle minus the missing 2×2 corner: 24 - 4 = 20 cm² — same answer.)*

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Problem 3)

Shape: Step-like, wider at the bottom.

Dimensions:

- Total width: 6 cm
- Total height: 4 cm
- Left side: 3 cm high
- Right side: 4 cm high
- Step: 2 cm wide at the top

✔ Split into two rectangles:

- Rectangle A (bottom): 3 cm (height) × 6 cm (width) → Area = 3 × 6 = 18 cm²
- Rectangle B (top right): 1 cm (height = 4–3) × 4 cm (width = 6–2) → Area = 1 × 4 = 4 cm²

> Why 4 cm wide? Because the step is 2 cm wide on the left, so the top rectangle spans the remaining 6 – 2 = 4 cm.

✔ Total Area = 18 + 4 = 22 cm²

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Problem 4)

Shape: Large rectangle with a smaller rectangle attached on the right side at the bottom.

Dimensions:

- Left part: 6 cm wide, 5 cm tall
- Right part: 4 cm wide (since total width is 10 cm, 10 – 6 = 4), 2 cm tall

✔ Split into two rectangles:

- Rectangle A (left): 6 cm × 5 cm → Area = 6 × 5 = 30 cm²
- Rectangle B (right bottom): 4 cm × 2 cm → Area = 4 × 2 = 8 cm²

✔ Total Area = 30 + 8 = 38 cm²

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## ✔ Final Answers:

1) Area = 5 cm²
2) Area = 20 cm²
3) Area = 22 cm²
4) Area = 38 cm²

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## 💡 Key Tip:
Always look for ways to divide the shape into simple rectangles. Make sure your rectangles don’t overlap and cover the entire shape. Use the given dimensions to figure out missing lengths if needed (like in Problem 3, we subtracted to find the top rectangle’s width).

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