Area and Perimeter of Rectangle - Free Printable

To solve the problems, we need to calculate the area and perimeter of each shape. Let's go through each problem step by step.

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Problem 1:

#### Shape:
- Dimensions:
- Top rectangle: \(10 \, \text{cm} \times 3 \, \text{cm}\)
- Bottom rectangle: \(5 \, \text{cm} \times 4 \, \text{cm}\)
- Right rectangle: \(7 \, \text{cm} \times 5 \, \text{cm}\)

#### Step 1: Calculate the Area
The area of the shape is the sum of the areas of the three rectangles:
\[
\text{Area} = (10 \times 3) + (5 \times 4) + (7 \times 5)
\]
\[
\text{Area} = 30 + 20 + 35 = 85 \, \text{cm}^2
\]

#### Step 2: Calculate the Perimeter
To find the perimeter, we need to determine the outer boundary of the shape. The perimeter is the sum of all the outer sides:
\[
\text{Perimeter} = 10 + 3 + 3 + 4 + 5 + 7 + 5 + 7 = 44 \, \text{cm}
\]

#### Final Answer for Problem 1:
\[
\boxed{85 \, \text{cm}^2, 44 \, \text{cm}}
\]

---

Problem 2:

#### Shape:
- Dimensions:
- Top rectangle: \(6 \, \text{mm} \times 6 \, \text{mm}\)
- Bottom rectangle: \(10 \, \text{mm} \times 8 \, \text{mm}\)

#### Step 1: Calculate the Area
The area of the shape is the sum of the areas of the two rectangles:
\[
\text{Area} = (6 \times 6) + (10 \times 8)
\]
\[
\text{Area} = 36 + 80 = 116 \, \text{mm}^2
\]

#### Step 2: Calculate the Perimeter
To find the perimeter, we need to determine the outer boundary of the shape. The perimeter is the sum of all the outer sides:
\[
\text{Perimeter} = 6 + 6 + 6 + 6 + 10 + 8 + 8 + 10 = 60 \, \text{mm}
\]

#### Final Answer for Problem 2:
\[
\boxed{116 \, \text{mm}^2, 60 \, \text{mm}}
\]

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Problem 3:

#### Shape:
- Dimensions:
- Left rectangle: \(5 \, \text{m} \times 6 \, \text{m}\)
- Middle rectangle: \(6 \, \text{m} \times 8 \, \text{m}\)
- Bottom rectangle: \(8 \, \text{m} \times 3 \, \text{m}\)

#### Step 1: Calculate the Area
The area of the shape is the sum of the areas of the three rectangles:
\[
\text{Area} = (5 \times 6) + (6 \times 8) + (8 \times 3)
\]
\[
\text{Area} = 30 + 48 + 24 = 102 \, \text{m}^2
\]

#### Step 2: Calculate the Perimeter
To find the perimeter, we need to determine the outer boundary of the shape. The perimeter is the sum of all the outer sides:
\[
\text{Perimeter} = 5 + 6 + 6 + 8 + 8 + 3 + 3 + 5 = 44 \, \text{m}
\]

#### Final Answer for Problem 3:
\[
\boxed{102 \, \text{m}^2, 44 \, \text{m}}
\]

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Problem 4:

#### Shape:
- Dimensions:
- Large rectangle: \(8 \, \text{cm} \times 6 \, \text{cm}\)
- Small rectangle: \(4 \, \text{cm} \times 5 \, \text{cm}\)

#### Step 1: Calculate the Area
The area of the shape is the area of the large rectangle minus the area of the small rectangle:
\[
\text{Area} = (8 \times 6) - (4 \times 5)
\]
\[
\text{Area} = 48 - 20 = 28 \, \text{cm}^2
\]

#### Step 2: Calculate the Perimeter
To find the perimeter, we need to determine the outer boundary of the shape. The perimeter is the sum of all the outer sides:
\[
\text{Perimeter} = 8 + 6 + 8 + 6 + 4 + 5 + 5 + 4 = 46 \, \text{cm}
\]

#### Final Answer for Problem 4:
\[
\boxed{28 \, \text{cm}^2, 46 \, \text{cm}}
\]

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Summary of Answers:

1. \(\boxed{85 \, \text{cm}^2, 44 \, \text{cm}}\)
2. \(\boxed{116 \, \text{mm}^2, 60 \, \text{mm}}\)
3. \(\boxed{102 \, \text{m}^2, 44 \, \text{m}}\)
4. \(\boxed{28 \, \text{cm}^2, 46 \, \text{cm}}\)