Educational math worksheet to calculate area and perimeter of geometric shapes.
Worksheet for calculating area and perimeter of various rectangles and squares with labeled dimensions in cm, mm, ft, and m.
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Step-by-step solution for: Area and Perimeter Worksheet - Teach On
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Show Answer Key & Explanations
Step-by-step solution for: Area and Perimeter Worksheet - Teach On
To solve the problem, we need to calculate the perimeter and area for each of the given figures. Let's go through each figure step by step.
1. Perimeter of a Rectangle/Square:
- Perimeter = \( 2 \times (\text{Length} + \text{Width}) \)
- For a square, since all sides are equal, Perimeter = \( 4 \times \text{Side} \).
2. Area of a Rectangle/Square:
- Area = \( \text{Length} \times \text{Width} \)
- For a square, Area = \( \text{Side} \times \text{Side} \).
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (7 \, \text{cm} + 4 \, \text{cm}) = 2 \times 11 \, \text{cm} = 22 \, \text{cm}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{sq cm}
\]
Answer:
- Perimeter = \( 22 \, \text{cm} \)
- Area = \( 28 \, \text{sq cm} \)
---
#### Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 3 \, \text{cm} = 12 \, \text{cm}
\]
#### Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 3 \, \text{cm} \times 3 \, \text{cm} = 9 \, \text{sq cm}
\]
Answer:
- Perimeter = \( 12 \, \text{cm} \)
- Area = \( 9 \, \text{sq cm} \)
---
#### Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 5 \, \text{mm} = 20 \, \text{mm}
\]
#### Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 5 \, \text{mm} \times 5 \, \text{mm} = 25 \, \text{sq mm}
\]
Answer:
- Perimeter = \( 20 \, \text{mm} \)
- Area = \( 25 \, \text{sq mm} \)
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (9 \, \text{mm} + 3 \, \text{mm}) = 2 \times 12 \, \text{mm} = 24 \, \text{mm}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 9 \, \text{mm} \times 3 \, \text{mm} = 27 \, \text{sq mm}
\]
Answer:
- Perimeter = \( 24 \, \text{mm} \)
- Area = \( 27 \, \text{sq mm} \)
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (8 \, \text{ft} + 2 \, \text{ft}) = 2 \times 10 \, \text{ft} = 20 \, \text{ft}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 8 \, \text{ft} \times 2 \, \text{ft} = 16 \, \text{sq ft}
\]
Answer:
- Perimeter = \( 20 \, \text{ft} \)
- Area = \( 16 \, \text{sq ft} \)
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (12 \, \text{ft} + 1 \, \text{ft}) = 2 \times 13 \, \text{ft} = 26 \, \text{ft}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 12 \, \text{ft} \times 1 \, \text{ft} = 12 \, \text{sq ft}
\]
Answer:
- Perimeter = \( 26 \, \text{ft} \)
- Area = \( 12 \, \text{sq ft} \)
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (2 \, \text{m} + 2 \, \text{m}) = 2 \times 4 \, \text{m} = 8 \, \text{m}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 2 \, \text{m} \times 2 \, \text{m} = 4 \, \text{sq m}
\]
Answer:
- Perimeter = \( 8 \, \text{m} \)
- Area = \( 4 \, \text{sq m} \)
---
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (9 \, \text{m} + 2 \, \text{m}) = 2 \times 11 \, \text{m} = 22 \, \text{m}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 9 \, \text{m} \times 2 \, \text{m} = 18 \, \text{sq m}
\]
Answer:
- Perimeter = \( 22 \, \text{m} \)
- Area = \( 18 \, \text{sq m} \)
---
1. Red Rectangle (7 cm × 4 cm):
- Perimeter: \( \boxed{22} \, \text{cm} \)
- Area: \( \boxed{28} \, \text{sq cm} \)
2. Green Square (3 cm × 3 cm):
- Perimeter: \( \boxed{12} \, \text{cm} \)
- Area: \( \boxed{9} \, \text{sq cm} \)
3. Yellow Square (5 mm × 5 mm):
- Perimeter: \( \boxed{20} \, \text{mm} \)
- Area: \( \boxed{25} \, \text{sq mm} \)
4. Blue Rectangle (9 mm × 3 mm):
- Perimeter: \( \boxed{24} \, \text{mm} \)
- Area: \( \boxed{27} \, \text{sq mm} \)
5. Green Rectangle (8 ft × 2 ft):
- Perimeter: \( \boxed{20} \, \text{ft} \)
- Area: \( \boxed{16} \, \text{sq ft} \)
6. Pink Rectangle (12 ft × 1 ft):
- Perimeter: \( \boxed{26} \, \text{ft} \)
- Area: \( \boxed{12} \, \text{sq ft} \)
7. Teal Rectangle (2 m × 2 m):
- Perimeter: \( \boxed{8} \, \text{m} \)
- Area: \( \boxed{4} \, \text{sq m} \)
8. Red Rectangle (9 m × 2 m):
- Perimeter: \( \boxed{22} \, \text{m} \)
- Area: \( \boxed{18} \, \text{sq m} \)
Formula Recap:
1. Perimeter of a Rectangle/Square:
- Perimeter = \( 2 \times (\text{Length} + \text{Width}) \)
- For a square, since all sides are equal, Perimeter = \( 4 \times \text{Side} \).
2. Area of a Rectangle/Square:
- Area = \( \text{Length} \times \text{Width} \)
- For a square, Area = \( \text{Side} \times \text{Side} \).
---
Figure 1: Red Rectangle (7 cm × 4 cm)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (7 \, \text{cm} + 4 \, \text{cm}) = 2 \times 11 \, \text{cm} = 22 \, \text{cm}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{sq cm}
\]
Answer:
- Perimeter = \( 22 \, \text{cm} \)
- Area = \( 28 \, \text{sq cm} \)
---
Figure 2: Green Square (3 cm × 3 cm)
#### Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 3 \, \text{cm} = 12 \, \text{cm}
\]
#### Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 3 \, \text{cm} \times 3 \, \text{cm} = 9 \, \text{sq cm}
\]
Answer:
- Perimeter = \( 12 \, \text{cm} \)
- Area = \( 9 \, \text{sq cm} \)
---
Figure 3: Yellow Square (5 mm × 5 mm)
#### Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 5 \, \text{mm} = 20 \, \text{mm}
\]
#### Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 5 \, \text{mm} \times 5 \, \text{mm} = 25 \, \text{sq mm}
\]
Answer:
- Perimeter = \( 20 \, \text{mm} \)
- Area = \( 25 \, \text{sq mm} \)
---
Figure 4: Blue Rectangle (9 mm × 3 mm)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (9 \, \text{mm} + 3 \, \text{mm}) = 2 \times 12 \, \text{mm} = 24 \, \text{mm}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 9 \, \text{mm} \times 3 \, \text{mm} = 27 \, \text{sq mm}
\]
Answer:
- Perimeter = \( 24 \, \text{mm} \)
- Area = \( 27 \, \text{sq mm} \)
---
Figure 5: Green Rectangle (8 ft × 2 ft)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (8 \, \text{ft} + 2 \, \text{ft}) = 2 \times 10 \, \text{ft} = 20 \, \text{ft}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 8 \, \text{ft} \times 2 \, \text{ft} = 16 \, \text{sq ft}
\]
Answer:
- Perimeter = \( 20 \, \text{ft} \)
- Area = \( 16 \, \text{sq ft} \)
---
Figure 6: Pink Rectangle (12 ft × 1 ft)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (12 \, \text{ft} + 1 \, \text{ft}) = 2 \times 13 \, \text{ft} = 26 \, \text{ft}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 12 \, \text{ft} \times 1 \, \text{ft} = 12 \, \text{sq ft}
\]
Answer:
- Perimeter = \( 26 \, \text{ft} \)
- Area = \( 12 \, \text{sq ft} \)
---
Figure 7: Teal Rectangle (2 m × 2 m)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (2 \, \text{m} + 2 \, \text{m}) = 2 \times 4 \, \text{m} = 8 \, \text{m}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 2 \, \text{m} \times 2 \, \text{m} = 4 \, \text{sq m}
\]
Answer:
- Perimeter = \( 8 \, \text{m} \)
- Area = \( 4 \, \text{sq m} \)
---
Figure 8: Red Rectangle (9 m × 2 m)
#### Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (9 \, \text{m} + 2 \, \text{m}) = 2 \times 11 \, \text{m} = 22 \, \text{m}
\]
#### Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 9 \, \text{m} \times 2 \, \text{m} = 18 \, \text{sq m}
\]
Answer:
- Perimeter = \( 22 \, \text{m} \)
- Area = \( 18 \, \text{sq m} \)
---
Final Answers:
1. Red Rectangle (7 cm × 4 cm):
- Perimeter: \( \boxed{22} \, \text{cm} \)
- Area: \( \boxed{28} \, \text{sq cm} \)
2. Green Square (3 cm × 3 cm):
- Perimeter: \( \boxed{12} \, \text{cm} \)
- Area: \( \boxed{9} \, \text{sq cm} \)
3. Yellow Square (5 mm × 5 mm):
- Perimeter: \( \boxed{20} \, \text{mm} \)
- Area: \( \boxed{25} \, \text{sq mm} \)
4. Blue Rectangle (9 mm × 3 mm):
- Perimeter: \( \boxed{24} \, \text{mm} \)
- Area: \( \boxed{27} \, \text{sq mm} \)
5. Green Rectangle (8 ft × 2 ft):
- Perimeter: \( \boxed{20} \, \text{ft} \)
- Area: \( \boxed{16} \, \text{sq ft} \)
6. Pink Rectangle (12 ft × 1 ft):
- Perimeter: \( \boxed{26} \, \text{ft} \)
- Area: \( \boxed{12} \, \text{sq ft} \)
7. Teal Rectangle (2 m × 2 m):
- Perimeter: \( \boxed{8} \, \text{m} \)
- Area: \( \boxed{4} \, \text{sq m} \)
8. Red Rectangle (9 m × 2 m):
- Perimeter: \( \boxed{22} \, \text{m} \)
- Area: \( \boxed{18} \, \text{sq m} \)
Parent Tip: Review the logic above to help your child master the concept of worksheet on area and perimeter.