area of compound shapes worksheet Archives - Mr-Mathematics.com - Free Printable

Problem: Calculate the shaded areas of the compound shapes provided.

#### Step-by-Step Solution:

We will calculate the shaded area for each shape (a, b, c, d, e) step by step.

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Shape (a):

The shape consists of two rectangles:
1. A larger rectangle with dimensions \(8 \, \text{cm} \times 5 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 3 \, \text{cm}\) (since the total width is 8 cm and the left part is 5 cm, the remaining width is \(8 - 5 = 3 \, \text{cm}\)).

#### Calculation:
- Area of the larger rectangle:
\[
\text{Area}_{\text{large}} = 8 \times 5 = 40 \, \text{cm}^2
\]
- Area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 4 \times 3 = 12 \, \text{cm}^2
\]
- Total shaded area:
\[
\text{Shaded Area} = \text{Area}_{\text{large}} + \text{Area}_{\text{small}} = 40 + 12 = 52 \, \text{cm}^2
\]

#### Answer for (a):
\[
\boxed{52 \, \text{cm}^2}
\]

---

Shape (b):

The shape consists of two rectangles:
1. A larger rectangle with dimensions \(7 \, \text{cm} \times 5 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 3 \, \text{cm}\) (since the total height is 7 cm and the top part is 4 cm, the remaining height is \(7 - 4 = 3 \, \text{cm}\)).

#### Calculation:
- Area of the larger rectangle:
\[
\text{Area}_{\text{large}} = 7 \times 5 = 35 \, \text{cm}^2
\]
- Area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 4 \times 3 = 12 \, \text{cm}^2
\]
- Total shaded area:
\[
\text{Shaded Area} = \text{Area}_{\text{large}} + \text{Area}_{\text{small}} = 35 + 12 = 47 \, \text{cm}^2
\]

#### Answer for (b):
\[
\boxed{47 \, \text{cm}^2}
\]

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Shape (c):

The shape is a large rectangle with a smaller rectangle removed from its center.
1. Dimensions of the large rectangle: \(13 \, \text{m} \times 4 \, \text{m}\).
2. Dimensions of the smaller rectangle: \(7 \, \text{m} \times 1 \, \text{m}\).

#### Calculation:
- Area of the large rectangle:
\[
\text{Area}_{\text{large}} = 13 \times 4 = 52 \, \text{m}^2
\]
- Area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = 7 \times 1 = 7 \, \text{m}^2
\]
- Shaded area (subtract the smaller rectangle from the larger rectangle):
\[
\text{Shaded Area} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} = 52 - 7 = 45 \, \text{m}^2
\]

#### Answer for (c):
\[
\boxed{45 \, \text{m}^2}
\]

---

Shape (d):

The shape is a "T"-shaped figure consisting of two rectangles:
1. A horizontal rectangle with dimensions \(20 \, \text{m} \times 5 \, \text{m}\).
2. A vertical rectangle with dimensions \(4 \, \text{m} \times 20 \, \text{m}\) (since the total height is 25 m and the top part is 5 m, the remaining height is \(25 - 5 = 20 \, \text{m}\)).

#### Calculation:
- Area of the horizontal rectangle:
\[
\text{Area}_{\text{horizontal}} = 20 \times 5 = 100 \, \text{m}^2
\]
- Area of the vertical rectangle:
\[
\text{Area}_{\text{vertical}} = 4 \times 20 = 80 \, \text{m}^2
\]
- Total shaded area:
\[
\text{Shaded Area} = \text{Area}_{\text{horizontal}} + \text{Area}_{\text{vertical}} = 100 + 80 = 180 \, \text{m}^2
\]

#### Answer for (d):
\[
\boxed{180 \, \text{m}^2}
\]

---

Shape (e):

The shape consists of three rectangles:
1. A top rectangle with dimensions \(14 \, \text{m} \times 4.5 \, \text{m}\).
2. A middle rectangle with dimensions \(9 \, \text{m} \times 3 \, \text{m}\).
3. A bottom rectangle with dimensions \(12 \, \text{m} \times 3 \, \text{m}\).

#### Calculation:
- Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 14 \times 4.5 = 63 \, \text{m}^2
\]
- Area of the middle rectangle:
\[
\text{Area}_{\text{middle}} = 9 \times 3 = 27 \, \text{m}^2
\]
- Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 12 \times 3 = 36 \, \text{m}^2
\]
- Total shaded area:
\[
\text{Shaded Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{middle}} + \text{Area}_{\text{bottom}} = 63 + 27 + 36 = 126 \, \text{m}^2
\]

#### Answer for (e):
\[
\boxed{126 \, \text{m}^2}
\]

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Final Answers:

\[
\boxed{52 \, \text{cm}^2, 47 \, \text{cm}^2, 45 \, \text{m}^2, 180 \, \text{m}^2, 126 \, \text{m}^2}
\]