Area of L Shapes Worksheets - Free Printable

To solve the problem of finding the area of L-shaped figures, we need to break each shape into simpler rectangular parts and then calculate the total area by summing up the areas of these rectangles. Let's go through each problem step by step.

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Problem 1:

- Dimensions:
- Top rectangle: \(6 \, \text{ft} \times 3 \, \text{ft}\)
- Bottom rectangle: \(3 \, \text{ft} \times 9 \, \text{ft}\)

#### Solution:
1. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 6 \, \text{ft} \times 3 \, \text{ft} = 18 \, \text{ft}^2
\]
2. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 3 \, \text{ft} \times 9 \, \text{ft} = 27 \, \text{ft}^2
\]
3. Total area:
\[
\text{Total Area} = 18 \, \text{ft}^2 + 27 \, \text{ft}^2 = 45 \, \text{ft}^2
\]

Answer for Problem 1: \(\boxed{45 \, \text{ft}^2}\)

---

Problem 2:

- Dimensions:
- Large rectangle: \(14 \, \text{m} \times 12 \, \text{m}\)
- Missing rectangle (cut-out): \(4 \, \text{m} \times 4 \, \text{m}\)

#### Solution:
1. Area of the large rectangle:
\[
\text{Area}_{\text{large}} = 14 \, \text{m} \times 12 \, \text{m} = 168 \, \text{m}^2
\]
2. Area of the missing rectangle:
\[
\text{Area}_{\text{missing}} = 4 \, \text{m} \times 4 \, \text{m} = 16 \, \text{m}^2
\]
3. Total area:
\[
\text{Total Area} = 168 \, \text{m}^2 - 16 \, \text{m}^2 = 152 \, \text{m}^2
\]

Answer for Problem 2: \(\boxed{152 \, \text{m}^2}\)

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Problem 3:

- Dimensions:
- Outer rectangle: \(14 \, \text{ft} \times 12 \, \text{ft}\)
- Inner rectangle (cut-out): \(8 \, \text{ft} \times 5 \, \text{ft}\)

#### Solution:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 14 \, \text{ft} \times 12 \, \text{ft} = 168 \, \text{ft}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 8 \, \text{ft} \times 5 \, \text{ft} = 40 \, \text{ft}^2
\]
3. Total area:
\[
\text{Total Area} = 168 \, \text{ft}^2 - 40 \, \text{ft}^2 = 128 \, \text{ft}^2
\]

Answer for Problem 3: \(\boxed{128 \, \text{ft}^2}\)

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Problem 4:

- Dimensions:
- Left rectangle: \(9 \, \text{cm} \times 3 \, \text{cm}\)
- Right rectangle: \(7 \, \text{cm} \times 2 \, \text{cm}\)

#### Solution:
1. Area of the left rectangle:
\[
\text{Area}_{\text{left}} = 9 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^2
\]
2. Area of the right rectangle:
\[
\text{Area}_{\text{right}} = 7 \, \text{cm} \times 2 \, \text{cm} = 14 \, \text{cm}^2
\]
3. Total area:
\[
\text{Total Area} = 27 \, \text{cm}^2 + 14 \, \text{cm}^2 = 41 \, \text{cm}^2
\]

Answer for Problem 4: \(\boxed{41 \, \text{cm}^2}\)

---

Problem 5:

- Dimensions:
- Outer rectangle: \(7 \, \text{m} \times 4 \, \text{m}\)
- Inner rectangle (cut-out): \(3 \, \text{m} \times 2 \, \text{m}\)

#### Solution:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 7 \, \text{m} \times 4 \, \text{m} = 28 \, \text{m}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 3 \, \text{m} \times 2 \, \text{m} = 6 \, \text{m}^2
\]
3. Total area:
\[
\text{Total Area} = 28 \, \text{m}^2 - 6 \, \text{m}^2 = 22 \, \text{m}^2
\]

Answer for Problem 5: \(\boxed{22 \, \text{m}^2}\)

---

Problem 6:

- Dimensions:
- Outer rectangle: \(9 \, \text{mm} \times 5 \, \text{mm}\)
- Inner rectangle (cut-out): \(4 \, \text{mm} \times 5 \, \text{mm}\)

#### Solution:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 9 \, \text{mm} \times 5 \, \text{mm} = 45 \, \text{mm}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 4 \, \text{mm} \times 5 \, \text{mm} = 20 \, \text{mm}^2
\]
3. Total area:
\[
\text{Total Area} = 45 \, \text{mm}^2 - 20 \, \text{mm}^2 = 25 \, \text{mm}^2
\]

Answer for Problem 6: \(\boxed{25 \, \text{mm}^2}\)

---

Problem 7:

- Dimensions:
- Left rectangle: \(12 \, \text{mm} \times 5 \, \text{mm}\)
- Bottom rectangle: \(8 \, \text{mm} \times 14 \, \text{mm}\)

#### Solution:
1. Area of the left rectangle:
\[
\text{Area}_{\text{left}} = 12 \, \text{mm} \times 5 \, \text{mm} = 60 \, \text{mm}^2
\]
2. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 8 \, \text{mm} \times 14 \, \text{mm} = 112 \, \text{mm}^2
\]
3. Total area:
\[
\text{Total Area} = 60 \, \text{mm}^2 + 112 \, \text{mm}^2 = 172 \, \text{mm}^2
\]

Answer for Problem 7: \(\boxed{172 \, \text{mm}^2}\)

---

Problem 8:

- Dimensions:
- Outer rectangle: \(12 \, \text{ft} \times 10 \, \text{ft}\)
- Inner rectangle (cut-out): \(6 \, \text{ft} \times 4 \, \text{ft}\)

#### Solution:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 12 \, \text{ft} \times 10 \, \text{ft} = 120 \, \text{ft}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 6 \, \text{ft} \times 4 \, \text{ft} = 24 \, \text{ft}^2
\]
3. Total area:
\[
\text{Total Area} = 120 \, \text{ft}^2 - 24 \, \text{ft}^2 = 96 \, \text{ft}^2
\]

Answer for Problem 8: \(\boxed{96 \, \text{ft}^2}\)

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Problem 9:

- Dimensions:
- Outer rectangle: \(11 \, \text{in} \times 9 \, \text{in}\)
- Inner rectangle (cut-out): \(6 \, \text{in} \times 5 \, \text{in}\)

#### Solution:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 11 \, \text{in} \times 9 \, \text{in} = 99 \, \text{in}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 6 \, \text{in} \times 5 \, \text{in} = 30 \, \text{in}^2
\]
3. Total area:
\[
\text{Total Area} = 99 \, \text{in}^2 - 30 \, \text{in}^2 = 69 \, \text{in}^2
\]

Answer for Problem 9: \(\boxed{69 \, \text{in}^2}\)

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Problem 10:

- Dimensions:
- Left rectangle: \(5 \, \text{mm} \times 3 \, \text{mm}\)
- Bottom rectangle: \(5 \, \text{mm} \times 2 \, \text{mm}\)

#### Solution:
1. Area of the left rectangle:
\[
\text{Area}_{\text{left}} = 5 \, \text{mm} \times 3 \, \text{mm} = 15 \, \text{mm}^2
\]
2. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 5 \, \text{mm} \times 2 \, \text{mm} = 10 \, \text{mm}^2
\]
3. Total area:
\[
\text{Total Area} = 15 \, \text{mm}^2 + 10 \, \text{mm}^2 = 25 \, \text{mm}^2
\]

Answer for Problem 10: \(\boxed{25 \, \text{mm}^2}\)

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Final Answers:

1. \(\boxed{45 \, \text{ft}^2}\)
2. \(\boxed{152 \, \text{m}^2}\)
3. \(\boxed{128 \, \text{ft}^2}\)
4. \(\boxed{41 \, \text{cm}^2}\)
5. \(\boxed{22 \, \text{m}^2}\)
6. \(\boxed{25 \, \text{mm}^2}\)
7. \(\boxed{172 \, \text{mm}^2}\)
8. \(\boxed{96 \, \text{ft}^2}\)
9. \(\boxed{69 \, \text{in}^2}\)
10. \(\boxed{25 \, \text{mm}^2}\)