Calculate the area and perimeter of the given geometric figures in this educational worksheet.
Area and Perimeter Worksheet with six colored rectangles and squares, each labeled with dimensions in cm, in, ft, and mm, and spaces to calculate perimeter and area.
JPG
1000×1643
100.5 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #710763
⭐
Show Answer Key & Explanations
Step-by-step solution for: Area and Perimeter worksheet for 4-6
▼
Show Answer Key & Explanations
Step-by-step solution for: Area and Perimeter worksheet for 4-6
To solve the problem, we need to calculate the perimeter and area for each of the given shapes. Let's go through each shape step by step.
1. Perimeter of a Rectangle/Square:
- Rectangle: \( P = 2 \times (\text{length} + \text{width}) \)
- Square: \( P = 4 \times \text{side} \)
2. Area of a Rectangle/Square:
- Rectangle: \( A = \text{length} \times \text{width} \)
- Square: \( A = \text{side} \times \text{side} \)
---
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (9 + 5) = 2 \times 14 = 28 \, \text{cm} \]
#### Area:
\[ A = \text{length} \times \text{width} = 9 \times 5 = 45 \, \text{cm}^2 \]
Answers:
- Perimeter: \( 28 \, \text{cm} \)
- Area: \( 45 \, \text{cm}^2 \)
---
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 6 = 24 \, \text{in} \]
#### Area:
\[ A = \text{side} \times \text{side} = 6 \times 6 = 36 \, \text{in}^2 \]
Answers:
- Perimeter: \( 24 \, \text{in} \)
- Area: \( 36 \, \text{in}^2 \)
---
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 4 = 16 \, \text{cm} \]
#### Area:
\[ A = \text{side} \times \text{side} = 4 \times 4 = 16 \, \text{cm}^2 \]
Answers:
- Perimeter: \( 16 \, \text{cm} \)
- Area: \( 16 \, \text{cm}^2 \)
---
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (7 + 4) = 2 \times 11 = 22 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 7 \times 4 = 28 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 22 \, \text{ft} \)
- Area: \( 28 \, \text{ft}^2 \)
---
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (15 + 8) = 2 \times 23 = 46 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 15 \times 8 = 120 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 46 \, \text{ft} \)
- Area: \( 120 \, \text{ft}^2 \)
---
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (13 + 9) = 2 \times 22 = 44 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 13 \times 9 = 117 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 44 \, \text{ft} \)
- Area: \( 117 \, \text{ft}^2 \)
---
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (27 + 8) = 2 \times 35 = 70 \, \text{in} \]
#### Area:
\[ A = \text{length} \times \text{width} = 27 \times 8 = 216 \, \text{in}^2 \]
Answers:
- Perimeter: \( 70 \, \text{in} \)
- Area: \( 216 \, \text{in}^2 \)
---
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 64 = 256 \, \text{mm} \]
#### Area:
\[ A = \text{side} \times \text{side} = 64 \times 64 = 4096 \, \text{mm}^2 \]
Answers:
- Perimeter: \( 256 \, \text{mm} \)
- Area: \( 4096 \, \text{mm}^2 \)
---
1. Yellow Rectangle (9 cm × 5 cm):
- Perimeter: \( 28 \, \text{cm} \)
- Area: \( 45 \, \text{cm}^2 \)
2. Orange Square (6 in × 6 in):
- Perimeter: \( 24 \, \text{in} \)
- Area: \( 36 \, \text{in}^2 \)
3. Pink Square (4 cm × 4 cm):
- Perimeter: \( 16 \, \text{cm} \)
- Area: \( 16 \, \text{cm}^2 \)
4. Yellow Rectangle (7 ft × 4 ft):
- Perimeter: \( 22 \, \text{ft} \)
- Area: \( 28 \, \text{ft}^2 \)
5. Blue Rectangle (15 ft × 8 ft):
- Perimeter: \( 46 \, \text{ft} \)
- Area: \( 120 \, \text{ft}^2 \)
6. Green Rectangle (13 ft × 9 ft):
- Perimeter: \( 44 \, \text{ft} \)
- Area: \( 117 \, \text{ft}^2 \)
7. Light Blue Rectangle (27 in × 8 in):
- Perimeter: \( 70 \, \text{in} \)
- Area: \( 216 \, \text{in}^2 \)
8. Purple Square (64 mm × 64 mm):
- Perimeter: \( 256 \, \text{mm} \)
- Area: \( 4096 \, \text{mm}^2 \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{Yellow Rectangle (9 cm × 5 cm)} & \text{Perimeter: } 28 \, \text{cm}, \, \text{Area: } 45 \, \text{cm}^2 \\
\text{Orange Square (6 in × 6 in)} & \text{Perimeter: } 24 \, \text{in}, \, \text{Area: } 36 \, \text{in}^2 \\
\text{Pink Square (4 cm × 4 cm)} & \text{Perimeter: } 16 \, \text{cm}, \, \text{Area: } 16 \, \text{cm}^2 \\
\text{Yellow Rectangle (7 ft × 4 ft)} & \text{Perimeter: } 22 \, \text{ft}, \, \text{Area: } 28 \, \text{ft}^2 \\
\text{Blue Rectangle (15 ft × 8 ft)} & \text{Perimeter: } 46 \, \text{ft}, \, \text{Area: } 120 \, \text{ft}^2 \\
\text{Green Rectangle (13 ft × 9 ft)} & \text{Perimeter: } 44 \, \text{ft}, \, \text{Area: } 117 \, \text{ft}^2 \\
\text{Light Blue Rectangle (27 in × 8 in)} & \text{Perimeter: } 70 \, \text{in}, \, \text{Area: } 216 \, \text{in}^2 \\
\text{Purple Square (64 mm × 64 mm)} & \text{Perimeter: } 256 \, \text{mm}, \, \text{Area: } 4096 \, \text{mm}^2 \\
\end{array}
}
\]
Formula Recap:
1. Perimeter of a Rectangle/Square:
- Rectangle: \( P = 2 \times (\text{length} + \text{width}) \)
- Square: \( P = 4 \times \text{side} \)
2. Area of a Rectangle/Square:
- Rectangle: \( A = \text{length} \times \text{width} \)
- Square: \( A = \text{side} \times \text{side} \)
---
Shape 1: Yellow Rectangle (9 cm × 5 cm)
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (9 + 5) = 2 \times 14 = 28 \, \text{cm} \]
#### Area:
\[ A = \text{length} \times \text{width} = 9 \times 5 = 45 \, \text{cm}^2 \]
Answers:
- Perimeter: \( 28 \, \text{cm} \)
- Area: \( 45 \, \text{cm}^2 \)
---
Shape 2: Orange Square (6 in × 6 in)
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 6 = 24 \, \text{in} \]
#### Area:
\[ A = \text{side} \times \text{side} = 6 \times 6 = 36 \, \text{in}^2 \]
Answers:
- Perimeter: \( 24 \, \text{in} \)
- Area: \( 36 \, \text{in}^2 \)
---
Shape 3: Pink Square (4 cm × 4 cm)
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 4 = 16 \, \text{cm} \]
#### Area:
\[ A = \text{side} \times \text{side} = 4 \times 4 = 16 \, \text{cm}^2 \]
Answers:
- Perimeter: \( 16 \, \text{cm} \)
- Area: \( 16 \, \text{cm}^2 \)
---
Shape 4: Yellow Rectangle (7 ft × 4 ft)
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (7 + 4) = 2 \times 11 = 22 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 7 \times 4 = 28 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 22 \, \text{ft} \)
- Area: \( 28 \, \text{ft}^2 \)
---
Shape 5: Blue Rectangle (15 ft × 8 ft)
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (15 + 8) = 2 \times 23 = 46 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 15 \times 8 = 120 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 46 \, \text{ft} \)
- Area: \( 120 \, \text{ft}^2 \)
---
Shape 6: Green Rectangle (13 ft × 9 ft)
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (13 + 9) = 2 \times 22 = 44 \, \text{ft} \]
#### Area:
\[ A = \text{length} \times \text{width} = 13 \times 9 = 117 \, \text{ft}^2 \]
Answers:
- Perimeter: \( 44 \, \text{ft} \)
- Area: \( 117 \, \text{ft}^2 \)
---
Shape 7: Light Blue Rectangle (27 in × 8 in)
#### Perimeter:
\[ P = 2 \times (\text{length} + \text{width}) = 2 \times (27 + 8) = 2 \times 35 = 70 \, \text{in} \]
#### Area:
\[ A = \text{length} \times \text{width} = 27 \times 8 = 216 \, \text{in}^2 \]
Answers:
- Perimeter: \( 70 \, \text{in} \)
- Area: \( 216 \, \text{in}^2 \)
---
Shape 8: Purple Square (64 mm × 64 mm)
#### Perimeter:
\[ P = 4 \times \text{side} = 4 \times 64 = 256 \, \text{mm} \]
#### Area:
\[ A = \text{side} \times \text{side} = 64 \times 64 = 4096 \, \text{mm}^2 \]
Answers:
- Perimeter: \( 256 \, \text{mm} \)
- Area: \( 4096 \, \text{mm}^2 \)
---
Final Answers:
1. Yellow Rectangle (9 cm × 5 cm):
- Perimeter: \( 28 \, \text{cm} \)
- Area: \( 45 \, \text{cm}^2 \)
2. Orange Square (6 in × 6 in):
- Perimeter: \( 24 \, \text{in} \)
- Area: \( 36 \, \text{in}^2 \)
3. Pink Square (4 cm × 4 cm):
- Perimeter: \( 16 \, \text{cm} \)
- Area: \( 16 \, \text{cm}^2 \)
4. Yellow Rectangle (7 ft × 4 ft):
- Perimeter: \( 22 \, \text{ft} \)
- Area: \( 28 \, \text{ft}^2 \)
5. Blue Rectangle (15 ft × 8 ft):
- Perimeter: \( 46 \, \text{ft} \)
- Area: \( 120 \, \text{ft}^2 \)
6. Green Rectangle (13 ft × 9 ft):
- Perimeter: \( 44 \, \text{ft} \)
- Area: \( 117 \, \text{ft}^2 \)
7. Light Blue Rectangle (27 in × 8 in):
- Perimeter: \( 70 \, \text{in} \)
- Area: \( 216 \, \text{in}^2 \)
8. Purple Square (64 mm × 64 mm):
- Perimeter: \( 256 \, \text{mm} \)
- Area: \( 4096 \, \text{mm}^2 \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{Yellow Rectangle (9 cm × 5 cm)} & \text{Perimeter: } 28 \, \text{cm}, \, \text{Area: } 45 \, \text{cm}^2 \\
\text{Orange Square (6 in × 6 in)} & \text{Perimeter: } 24 \, \text{in}, \, \text{Area: } 36 \, \text{in}^2 \\
\text{Pink Square (4 cm × 4 cm)} & \text{Perimeter: } 16 \, \text{cm}, \, \text{Area: } 16 \, \text{cm}^2 \\
\text{Yellow Rectangle (7 ft × 4 ft)} & \text{Perimeter: } 22 \, \text{ft}, \, \text{Area: } 28 \, \text{ft}^2 \\
\text{Blue Rectangle (15 ft × 8 ft)} & \text{Perimeter: } 46 \, \text{ft}, \, \text{Area: } 120 \, \text{ft}^2 \\
\text{Green Rectangle (13 ft × 9 ft)} & \text{Perimeter: } 44 \, \text{ft}, \, \text{Area: } 117 \, \text{ft}^2 \\
\text{Light Blue Rectangle (27 in × 8 in)} & \text{Perimeter: } 70 \, \text{in}, \, \text{Area: } 216 \, \text{in}^2 \\
\text{Purple Square (64 mm × 64 mm)} & \text{Perimeter: } 256 \, \text{mm}, \, \text{Area: } 4096 \, \text{mm}^2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter worksheet 4th grade.