Find the area of composite shapes in this math worksheet.

To solve the problem of finding the area of the composite shapes, we need to break each shape into simpler geometric figures (like rectangles and triangles) and then calculate their areas individually. Finally, we sum up the areas of these simpler shapes to get the total area of the composite shape.

Problem 1:

The first composite shape consists of two rectangles.

#### Step 1: Identify the dimensions of the rectangles.
- The larger rectangle has dimensions \(10 \, \text{m} \times 5 \, \text{m}\).
- The smaller rectangle has dimensions \(3 \, \text{m} \times 5 \, \text{m}\).

#### Step 2: Calculate the area of each rectangle.
- Area of the larger rectangle:
\[
\text{Area}_{\text{large}} = 10 \, \text{m} \times 5 \, \text{m} = 50 \, \text{m}^2
\]
- Area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 3 \, \text{m} \times 5 \, \text{m} = 15 \, \text{m}^2
\]

#### Step 3: Sum the areas of the two rectangles.
\[
\text{Total Area} = \text{Area}_{\text{large}} + \text{Area}_{\text{small}} = 50 \, \text{m}^2 + 15 \, \text{m}^2 = 65 \, \text{m}^2
\]

Final Answer for Problem 1:

\[
\boxed{65 \, \text{m}^2}
\]

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Problem 2:

The second composite shape consists of a rectangle and a triangle.

#### Step 1: Identify the dimensions of the rectangle and the triangle.
- The rectangle has dimensions \(8 \, \text{cm} \times 9 \, \text{cm}\).
- The triangle has a base of \(6 \, \text{cm}\) and a height of \(8 \, \text{cm}\) (same as the height of the rectangle).

#### Step 2: Calculate the area of the rectangle.
\[
\text{Area}_{\text{rectangle}} = 8 \, \text{cm} \times 9 \, \text{cm} = 72 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the triangle.
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \, \text{cm} \times 8 \, \text{cm} = \frac{1}{2} \times 48 \, \text{cm}^2 = 24 \, \text{cm}^2
\]

#### Step 4: Sum the areas of the rectangle and the triangle.
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 72 \, \text{cm}^2 + 24 \, \text{cm}^2 = 96 \, \text{cm}^2
\]

Final Answer for Problem 2:

\[
\boxed{96 \, \text{cm}^2}
\]

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Problem 3:

The third composite shape consists of two rectangles.

#### Step 1: Identify the dimensions of the rectangles.
- The larger rectangle has dimensions \(6 \, \text{m} \times 4 \, \text{m}\).
- The smaller rectangle has dimensions \(5 \, \text{m} \times 6 \, \text{m}\).

#### Step 2: Calculate the area of each rectangle.
- Area of the larger rectangle:
\[
\text{Area}_{\text{large}} = 6 \, \text{m} \times 4 \, \text{m} = 24 \, \text{m}^2
\]
- Area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 5 \, \text{m} \times 6 \, \text{m} = 30 \, \text{m}^2
\]

#### Step 3: Sum the areas of the two rectangles.
\[
\text{Total Area} = \text{Area}_{\text{large}} + \text{Area}_{\text{small}} = 24 \, \text{m}^2 + 30 \, \text{m}^2 = 54 \, \text{m}^2
\]

Final Answer for Problem 3:

\[
\boxed{54 \, \text{m}^2}
\]

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Summary of Answers:

1. \(\boxed{65 \, \text{m}^2}\)
2. \(\boxed{96 \, \text{cm}^2}\)
3. \(\boxed{54 \, \text{m}^2}\)