Calculate the area of compound shapes with given dimensions.

To solve the problem of finding the area of compound shapes, we break each shape into rectangles (or squares), calculate the area of each rectangle using the formula:

> Area = length × width

Then, we add the areas of the individual rectangles to get the total area of the compound shape.

Let’s solve each part one by one.

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a)

This shape can be split into two rectangles:

- Bottom rectangle: 6 cm (width) × 4 cm (height) → Area = 6 × 4 = 24 cm²
- Top-right rectangle: 2 cm (width) × 8 cm (height) → Area = 2 × 8 = 16 cm²

✔ Total Area = 24 + 16 = 40 cm²

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b)

Split into two rectangles:

- Left rectangle: 7 cm (height) × 4 cm (width) → Area = 7 × 4 = 28 cm²
- Right rectangle: 3 cm (width) × (12 - 4) = 8 cm (height) → Area = 3 × 8 = 24 cm²

✔ Total Area = 28 + 24 = 52 cm²

*(Note: The total width is 12 cm. Since left part is 4 cm wide, the right part is 12 - 4 = 8 cm high.)*

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c)

Split into two rectangles:

- Top rectangle: 6 cm (width) × 4 cm (height) → Area = 6 × 4 = 24 cm²
- Bottom rectangle: 7 cm (width) × 11 cm (height) → Area = 7 × 11 = 77 cm²

✔ Total Area = 24 + 77 = 101 cm²

*(Note: The bottom rectangle is 7 cm wide and 11 cm tall — this includes the full height of the shape.)*

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d)

Split into two rectangles:

- Bottom rectangle: 16 cm (width) × 6 cm (height) → Area = 16 × 6 = 96 cm²
- Top rectangle: (16 - 6) = 10 cm (width) × 8 cm (height) → Area = 10 × 8 = 80 cm²

✔ Total Area = 96 + 80 = 176 cm²

*(Note: The top part only spans the remaining width after subtracting the 6 cm “notch” on the right. So width = 16 - 6 = 10 cm.)*

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## ✔ Final Answers:

- a) 40 cm²
- b) 52 cm²
- c) 101 cm²
- d) 176 cm²

You can fill these in the boxes on your worksheet! Let me know if you’d like a diagram for any of them.