Grade 6 Area Worksheet 1: Calculate the area of irregular shapes with given dimensions.

To solve the problem of finding the area for each shape, we will break down each figure into simpler geometric shapes (rectangles) and calculate their areas individually. Then, we will sum up the areas to get the total area for each figure.

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Problem 1:

The given shape can be divided into two rectangles:
1. A rectangle with dimensions \(8 \, \text{m} \times 8 \, \text{m}\).
2. A rectangle with dimensions \(3 \, \text{m} \times 12 \, \text{m}\).

#### Step 1: Calculate the area of the first rectangle.
\[
\text{Area}_1 = 8 \, \text{m} \times 8 \, \text{m} = 64 \, \text{m}^2
\]

#### Step 2: Calculate the area of the second rectangle.
\[
\text{Area}_2 = 3 \, \text{m} \times 12 \, \text{m} = 36 \, \text{m}^2
\]

#### Step 3: Sum the areas of the two rectangles.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 64 \, \text{m}^2 + 36 \, \text{m}^2 = 100 \, \text{m}^2
\]

Answer for Problem 1:
\[
\boxed{100}
\]

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Problem 2:

The given shape can be divided into two rectangles:
1. A rectangle with dimensions \(20 \, \text{cm} \times 18 \, \text{cm}\).
2. A smaller rectangle with dimensions \(5 \, \text{cm} \times 10 \, \text{cm}\).

#### Step 1: Calculate the area of the first rectangle.
\[
\text{Area}_1 = 20 \, \text{cm} \times 18 \, \text{cm} = 360 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the second rectangle.
\[
\text{Area}_2 = 5 \, \text{cm} \times 10 \, \text{cm} = 50 \, \text{cm}^2
\]

#### Step 3: Subtract the area of the smaller rectangle from the larger rectangle (since it is a cut-out section).
\[
\text{Total Area} = \text{Area}_1 - \text{Area}_2 = 360 \, \text{cm}^2 - 50 \, \text{cm}^2 = 310 \, \text{cm}^2
\]

Answer for Problem 2:
\[
\boxed{310}
\]

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Problem 3:

The given shape can be divided into three rectangles:
1. A large rectangle with dimensions \(10 \, \text{m} \times 14 \, \text{m}\).
2. A smaller rectangle with dimensions \(5 \, \text{m} \times 5 \, \text{m}\) (cut-out section).
3. Another smaller rectangle with dimensions \(4 \, \text{m} \times 5 \, \text{m}\) (cut-out section).

#### Step 1: Calculate the area of the large rectangle.
\[
\text{Area}_1 = 10 \, \text{m} \times 14 \, \text{m} = 140 \, \text{m}^2
\]

#### Step 2: Calculate the area of the first cut-out rectangle.
\[
\text{Area}_2 = 5 \, \text{m} \times 5 \, \text{m} = 25 \, \text{m}^2
\]

#### Step 3: Calculate the area of the second cut-out rectangle.
\[
\text{Area}_3 = 4 \, \text{m} \times 5 \, \text{m} = 20 \, \text{m}^2
\]

#### Step 4: Subtract the areas of the cut-out sections from the large rectangle.
\[
\text{Total Area} = \text{Area}_1 - (\text{Area}_2 + \text{Area}_3) = 140 \, \text{m}^2 - (25 \, \text{m}^2 + 20 \, \text{m}^2) = 140 \, \text{m}^2 - 45 \, \text{m}^2 = 95 \, \text{m}^2
\]

Answer for Problem 3:
\[
\boxed{95}
\]

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Final Answers:

1. \(\boxed{100}\)
2. \(\boxed{310}\)
3. \(\boxed{95}\)