Perimeter and Area Practice Worksheet with Rectangles and Measurements.
Worksheet with nine rectangles showing dimensions for calculating perimeter and area.
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Step-by-step solution for: Perimeter and Area Worksheet for 6th Grade | Lesson Planet
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Show Answer Key & Explanations
Step-by-step solution for: Perimeter and Area Worksheet for 6th Grade | Lesson Planet
The image you uploaded contains a worksheet titled "Perimeter and Area". The task involves calculating the perimeter and area of various rectangles and squares. Below, I will solve each problem step by step.
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1. Perimeter of a Rectangle/Square:
- For a rectangle: \( P = 2 \times (\text{length} + \text{width}) \)
- For a square: \( P = 4 \times \text{side length} \)
2. Area of a Rectangle/Square:
- For a rectangle: \( A = \text{length} \times \text{width} \)
- For a square: \( A = \text{side length}^2 \)
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#### Problem 1:
- Dimensions: Length = 27 cm, Width = 8 cm
- Perimeter: \( P = 2 \times (27 + 8) = 2 \times 35 = 70 \) cm
- Area: \( A = 27 \times 8 = 216 \) cm²
#### Problem 2:
- Dimensions: Length = 21 cm, Width = 16 cm
- Perimeter: \( P = 2 \times (21 + 16) = 2 \times 37 = 74 \) cm
- Area: \( A = 21 \times 16 = 336 \) cm²
#### Problem 3:
- Dimensions: Side = 10 cm (square)
- Perimeter: \( P = 4 \times 10 = 40 \) cm
- Area: \( A = 10^2 = 100 \) cm²
#### Problem 4:
- Dimensions: Length = 11 cm, Width = 9 cm
- Perimeter: \( P = 2 \times (11 + 9) = 2 \times 20 = 40 \) cm
- Area: \( A = 11 \times 9 = 99 \) cm²
#### Problem 5:
- Dimensions: Length = 15 cm, Width = 8 cm
- Perimeter: \( P = 2 \times (15 + 8) = 2 \times 23 = 46 \) cm
- Area: \( A = 15 \times 8 = 120 \) cm²
#### Problem 6:
- Dimensions: Length = 15 cm, Width = 15 cm (square)
- Perimeter: \( P = 4 \times 15 = 60 \) cm
- Area: \( A = 15^2 = 225 \) cm²
#### Problem 7:
- Dimensions: Length = 13 cm, Width = 11 cm
- Perimeter: \( P = 2 \times (13 + 11) = 2 \times 24 = 48 \) cm
- Area: \( A = 13 \times 11 = 143 \) cm²
#### Problem 8:
- Dimensions: Length = 20 cm, Width = 19 cm
- Perimeter: \( P = 2 \times (20 + 19) = 2 \times 39 = 78 \) cm
- Area: \( A = 20 \times 19 = 380 \) cm²
#### Problem 9:
- Dimensions: Length = 20 cm, Width = 26 cm
- Perimeter: \( P = 2 \times (20 + 26) = 2 \times 46 = 92 \) cm
- Area: \( A = 20 \times 26 = 520 \) cm²
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| Problem | Perimeter (cm) | Area (cm²) |
|---------|----------------|------------|
| 1 | 70 | 216 |
| 2 | 74 | 336 |
| 3 | 40 | 100 |
| 4 | 40 | 99 |
| 5 | 46 | 120 |
| 6 | 60 | 225 |
| 7 | 48 | 143 |
| 8 | 78 | 380 |
| 9 | 92 | 520 |
---
\[
\boxed{
\begin{array}{c|c|c}
\text{Problem} & \text{Perimeter (cm)} & \text{Area (cm²)} \\
\hline
1 & 70 & 216 \\
2 & 74 & 336 \\
3 & 40 & 100 \\
4 & 40 & 99 \\
5 & 46 & 120 \\
6 & 60 & 225 \\
7 & 48 & 143 \\
8 & 78 & 380 \\
9 & 92 & 520 \\
\end{array}
}
\]
---
Key Formulas:
1. Perimeter of a Rectangle/Square:
- For a rectangle: \( P = 2 \times (\text{length} + \text{width}) \)
- For a square: \( P = 4 \times \text{side length} \)
2. Area of a Rectangle/Square:
- For a rectangle: \( A = \text{length} \times \text{width} \)
- For a square: \( A = \text{side length}^2 \)
---
Solutions:
#### Problem 1:
- Dimensions: Length = 27 cm, Width = 8 cm
- Perimeter: \( P = 2 \times (27 + 8) = 2 \times 35 = 70 \) cm
- Area: \( A = 27 \times 8 = 216 \) cm²
#### Problem 2:
- Dimensions: Length = 21 cm, Width = 16 cm
- Perimeter: \( P = 2 \times (21 + 16) = 2 \times 37 = 74 \) cm
- Area: \( A = 21 \times 16 = 336 \) cm²
#### Problem 3:
- Dimensions: Side = 10 cm (square)
- Perimeter: \( P = 4 \times 10 = 40 \) cm
- Area: \( A = 10^2 = 100 \) cm²
#### Problem 4:
- Dimensions: Length = 11 cm, Width = 9 cm
- Perimeter: \( P = 2 \times (11 + 9) = 2 \times 20 = 40 \) cm
- Area: \( A = 11 \times 9 = 99 \) cm²
#### Problem 5:
- Dimensions: Length = 15 cm, Width = 8 cm
- Perimeter: \( P = 2 \times (15 + 8) = 2 \times 23 = 46 \) cm
- Area: \( A = 15 \times 8 = 120 \) cm²
#### Problem 6:
- Dimensions: Length = 15 cm, Width = 15 cm (square)
- Perimeter: \( P = 4 \times 15 = 60 \) cm
- Area: \( A = 15^2 = 225 \) cm²
#### Problem 7:
- Dimensions: Length = 13 cm, Width = 11 cm
- Perimeter: \( P = 2 \times (13 + 11) = 2 \times 24 = 48 \) cm
- Area: \( A = 13 \times 11 = 143 \) cm²
#### Problem 8:
- Dimensions: Length = 20 cm, Width = 19 cm
- Perimeter: \( P = 2 \times (20 + 19) = 2 \times 39 = 78 \) cm
- Area: \( A = 20 \times 19 = 380 \) cm²
#### Problem 9:
- Dimensions: Length = 20 cm, Width = 26 cm
- Perimeter: \( P = 2 \times (20 + 26) = 2 \times 46 = 92 \) cm
- Area: \( A = 20 \times 26 = 520 \) cm²
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Final Answers:
| Problem | Perimeter (cm) | Area (cm²) |
|---------|----------------|------------|
| 1 | 70 | 216 |
| 2 | 74 | 336 |
| 3 | 40 | 100 |
| 4 | 40 | 99 |
| 5 | 46 | 120 |
| 6 | 60 | 225 |
| 7 | 48 | 143 |
| 8 | 78 | 380 |
| 9 | 92 | 520 |
---
Boxed Final Answer:
\[
\boxed{
\begin{array}{c|c|c}
\text{Problem} & \text{Perimeter (cm)} & \text{Area (cm²)} \\
\hline
1 & 70 & 216 \\
2 & 74 & 336 \\
3 & 40 & 100 \\
4 & 40 & 99 \\
5 & 46 & 120 \\
6 & 60 & 225 \\
7 & 48 & 143 \\
8 & 78 & 380 \\
9 & 92 & 520 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of 6th grade area and perimeter worksheet.