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 figures to get the total area of the composite shape.
Problem 1:
The shape is a combination of two rectangles.
#### Step 1: Identify the rectangles
- The top rectangle has dimensions \(2 \, \text{m} \times 8 \, \text{m}\).
- The bottom rectangle has dimensions \(8 \, \text{m} \times 2 \, \text{m}\).
#### Step 2: Calculate the area of each rectangle
- Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 2 \, \text{m} \times 8 \, \text{m} = 16 \, \text{m}^2
\]
- Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 8 \, \text{m} \times 2 \, \text{m} = 16 \, \text{m}^2
\]
#### Step 3: Sum the areas
\[
\text{Total Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 16 \, \text{m}^2 + 16 \, \text{m}^2 = 32 \, \text{m}^2
\]
Final Answer for Problem 1:
\[
\boxed{32}
\]
---
Problem 2:
The shape is a combination of a triangle and a rectangle.
#### Step 1: Identify the shapes
- The top part is a triangle with base \(6 \, \text{m}\) and height \(4 \, \text{m}\).
- The bottom part is a rectangle with dimensions \(6 \, \text{m} \times 3 \, \text{m}\).
#### Step 2: Calculate the area of the triangle
The formula for the area of a triangle is:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 6 \, \text{m} \times 4 \, \text{m} = \frac{1}{2} \times 24 \, \text{m}^2 = 12 \, \text{m}^2
\]
#### Step 3: Calculate the area of the rectangle
\[
\text{Area}_{\text{rectangle}} = 6 \, \text{m} \times 3 \, \text{m} = 18 \, \text{m}^2
\]
#### Step 4: Sum the areas
\[
\text{Total Area} = \text{Area}_{\text{triangle}} + \text{Area}_{\text{rectangle}} = 12 \, \text{m}^2 + 18 \, \text{m}^2 = 30 \, \text{m}^2
\]
Final Answer for Problem 2:
\[
\boxed{30}
\]
---
Problem 3:
The shape is a combination of two rectangles.
#### Step 1: Identify the rectangles
- The left rectangle has dimensions \(2 \, \text{m} \times 8 \, \text{m}\).
- The right rectangle has dimensions \(6 \, \text{m} \times 3 \, \text{m}\).
#### Step 2: Calculate the area of each rectangle
- Area of the left rectangle:
\[
\text{Area}_{\text{left}} = 2 \, \text{m} \times 8 \, \text{m} = 16 \, \text{m}^2
\]
- Area of the right rectangle:
\[
\text{Area}_{\text{right}} = 6 \, \text{m} \times 3 \, \text{m} = 18 \, \text{m}^2
\]
#### Step 3: Sum the areas
\[
\text{Total Area} = \text{Area}_{\text{left}} + \text{Area}_{\text{right}} = 16 \, \text{m}^2 + 18 \, \text{m}^2 = 34 \, \text{m}^2
\]
Final Answer for Problem 3:
\[
\boxed{34}
\]
---
Summary of Answers:
1. \(\boxed{32}\)
2. \(\boxed{30}\)
3. \(\boxed{34}\)
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet 6th grade.
