Grade 6 Area Worksheet 1 with three geometric figures requiring area calculation.

Let's solve each of the three area problems step by step. These are composite shapes (made up of rectangles), so we'll break them down into simpler rectangles, calculate their areas, and then add or subtract as needed.

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Problem 1

Shape: An L-shaped figure with dimensions:

- Total base: 12 m
- Left vertical side: 8 m
- Right horizontal side: 3 m
- Top horizontal segment: 8 m

We can split this shape into two rectangles:

#### Rectangle A (Left part):
- Width = 4 m (since total width is 12 m, and right part is 8 m → 12 - 8 = 4)
- Height = 8 m
→ Area = 4 × 8 = 32 m²

#### Rectangle B (Right part):
- Width = 8 m
- Height = 3 m
→ Area = 8 × 3 = 24 m²

#### Total Area:
32 + 24 = 56 m²

✔ Answer: 56 m²

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Problem 2

Shape: A rectangle with a "bite" taken out on the top-right.

Dimensions:
- Total width: 18 cm
- Total height: 20 cm
- The missing rectangle has:
- Width: 5 cm
- Height: 10 cm (from the top)

We can think of this as:

#### Big Rectangle (whole shape if complete):
- 18 cm × 20 cm = 360 cm²

#### Missing Rectangle (cut-out):
- 5 cm × 10 cm = 50 cm²

#### Actual Area:
360 - 50 = 310 cm²

✔ Answer: 310 cm²

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Problem 3

Shape: A rectangle with a rectangular cut-out in the middle.

Dimensions:
- Outer rectangle: 14 m wide, 10 m high
- Cut-out: 5 m wide, 4 m high (centered horizontally)

We can calculate:

#### Outer Rectangle Area:
14 × 10 = 140 m²

#### Cut-out Area:
5 × 4 = 20 m²

#### Actual Area:
140 - 20 = 120 m²

✔ Answer: 120 m²

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✔ Final Answers:

1. 56 m²
2. 310 cm²
3. 120 m²

Let me know if you'd like a visual breakdown!