Grade 6 Area and Perimeter Worksheets | Free Math Worksheets - Free Printable

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

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Problem 1:

The first shape is a composite rectangle with a smaller rectangle removed from one corner.

#### Step 1: Identify the dimensions
- The large rectangle has dimensions \(9 \, \text{m} \times 7 \, \text{m}\).
- The smaller rectangle that is removed has dimensions \(3 \, \text{m} \times 3 \, \text{m}\).

#### Step 2: Calculate the area of the large rectangle
\[
\text{Area of large rectangle} = \text{length} \times \text{width} = 9 \, \text{m} \times 7 \, \text{m} = 63 \, \text{m}^2
\]

#### Step 3: Calculate the area of the smaller rectangle
\[
\text{Area of smaller rectangle} = \text{length} \times \text{width} = 3 \, \text{m} \times 3 \, \text{m} = 9 \, \text{m}^2
\]

#### Step 4: Subtract the area of the smaller rectangle from the area of the large rectangle
\[
\text{Total area} = \text{Area of large rectangle} - \text{Area of smaller rectangle} = 63 \, \text{m}^2 - 9 \, \text{m}^2 = 54 \, \text{m}^2
\]

#### Final Answer for Problem 1:
\[
\boxed{54}
\]

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Problem 2:

The second shape is a composite rectangle with a smaller rectangle removed from one side.

#### Step 1: Identify the dimensions
- The large rectangle has dimensions \(6 \, \text{m} \times 6 \, \text{m}\).
- The smaller rectangle that is removed has dimensions \(3 \, \text{m} \times 1 \, \text{m}\).

#### Step 2: Calculate the area of the large rectangle
\[
\text{Area of large rectangle} = \text{length} \times \text{width} = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2
\]

#### Step 3: Calculate the area of the smaller rectangle
\[
\text{Area of smaller rectangle} = \text{length} \times \text{width} = 3 \, \text{m} \times 1 \, \text{m} = 3 \, \text{m}^2
\]

#### Step 4: Subtract the area of the smaller rectangle from the area of the large rectangle
\[
\text{Total area} = \text{Area of large rectangle} - \text{Area of smaller rectangle} = 36 \, \text{m}^2 - 3 \, \text{m}^2 = 33 \, \text{m}^2
\]

#### Final Answer for Problem 2:
\[
\boxed{33}
\]

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Problem 3:

The third shape consists of a rectangle and two right triangles.

#### Step 1: Identify the dimensions
- The rectangle has dimensions \(4 \, \text{m} \times 4 \, \text{m}\).
- Each triangle has a base of \(4 \, \text{m}\) and a height of \(4 \, \text{m}\).

#### Step 2: Calculate the area of the rectangle
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 4 \, \text{m} \times 4 \, \text{m} = 16 \, \text{m}^2
\]

#### Step 3: Calculate the area of one triangle
The formula for the area of a triangle is:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For one triangle:
\[
\text{Area of one triangle} = \frac{1}{2} \times 4 \, \text{m} \times 4 \, \text{m} = \frac{1}{2} \times 16 \, \text{m}^2 = 8 \, \text{m}^2
\]

#### Step 4: Calculate the total area of the two triangles
\[
\text{Total area of two triangles} = 2 \times 8 \, \text{m}^2 = 16 \, \text{m}^2
\]

#### Step 5: Add the area of the rectangle and the total area of the two triangles
\[
\text{Total area} = \text{Area of rectangle} + \text{Total area of two triangles} = 16 \, \text{m}^2 + 16 \, \text{m}^2 = 32 \, \text{m}^2
\]

#### Final Answer for Problem 3:
\[
\boxed{32}
\]

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Final Answers:

1. \(\boxed{54}\)
2. \(\boxed{33}\)
3. \(\boxed{32}\)