Area of Shaded Region Worksheet (rectangles and triangles) - Free Printable

To solve the problem, we need to calculate the shaded areas in each of the given figures. Let's go through each part step by step.

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Part (a)

#### Given:
- Outer rectangle: Length = 12 cm, Width = 5 cm
- Inner rectangle: Length = 8 cm, Width = 3 cm

#### Solution:
The shaded area is the area of the outer rectangle minus the area of the inner rectangle.

1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = \text{Length} \times \text{Width} = 12 \, \text{cm} \times 5 \, \text{cm} = 60 \, \text{cm}^2
\]

2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = \text{Length} \times \text{Width} = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2
\]

3. Shaded area:
\[
\text{Shaded area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 60 \, \text{cm}^2 - 24 \, \text{cm}^2 = 36 \, \text{cm}^2
\]

#### Final Answer for Part (a):
\[
\boxed{36}
\]

---

Part (b)

#### Given:
- Outer rectangle: Length = 36 m, Width = 28 m
- Inner shape: A combination of a rectangle and two right triangles.

#### Solution:
The shaded area is the area of the outer rectangle minus the area of the inner shape.

1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = \text{Length} \times \text{Width} = 36 \, \text{m} \times 28 \, \text{m} = 1008 \, \text{m}^2
\]

2. Area of the inner shape:
- The inner shape consists of a rectangle and two right triangles.
- Rectangle: Length = 18 m, Width = 7 m
\[
\text{Area}_{\text{rectangle}} = 18 \, \text{m} \times 7 \, \text{m} = 126 \, \text{m}^2
\]
- Right triangle 1: Base = 13 m, Height = 7 m
\[
\text{Area}_{\text{triangle 1}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 13 \, \text{m} \times 7 \, \text{m} = 45.5 \, \text{m}^2
\]
- Right triangle 2: Base = 11 m, Height = 6 m
\[
\text{Area}_{\text{triangle 2}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 11 \, \text{m} \times 6 \, \text{m} = 33 \, \text{m}^2
\]

3. Total area of the inner shape:
\[
\text{Area}_{\text{inner}} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle 1}} + \text{Area}_{\text{triangle 2}} = 126 \, \text{m}^2 + 45.5 \, \text{m}^2 + 33 \, \text{m}^2 = 204.5 \, \text{m}^2
\]

4. Shaded area:
\[
\text{Shaded area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 1008 \, \text{m}^2 - 204.5 \, \text{m}^2 = 803.5 \, \text{m}^2
\]

#### Final Answer for Part (b):
\[
\boxed{803.5}
\]

---

Part (c)

#### Given:
- Trapezoid: Bases = 6 cm and 8 cm, Height = 3 cm
- Triangle: Base = 3 cm, Height = 3 cm

#### Solution:
The shaded area is the area of the trapezoid minus the area of the triangle.

1. Area of the trapezoid:
\[
\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} = \frac{1}{2} \times (6 \, \text{cm} + 8 \, \text{cm}) \times 3 \, \text{cm} = \frac{1}{2} \times 14 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]

2. Area of the triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 3 \, \text{cm} \times 3 \, \text{cm} = 4.5 \, \text{cm}^2
\]

3. Shaded area:
\[
\text{Shaded area} = \text{Area}_{\text{trapezoid}} - \text{Area}_{\text{triangle}} = 21 \, \text{cm}^2 - 4.5 \, \text{cm}^2 = 16.5 \, \text{cm}^2
\]

#### Final Answer for Part (c):
\[
\boxed{16.5}
\]

---

Part (d)

#### Given:
- Rectangle: Length = 12 cm, Width = 4 cm
- Triangle: Base = 9 cm, Height = 4 cm

#### Solution:
The shaded area is the area of the rectangle minus the area of the triangle.

1. Area of the rectangle:
\[
\text{Area}_{\text{rectangle}} = \text{Length} \times \text{Width} = 12 \, \text{cm} \times 4 \, \text{cm} = 48 \, \text{cm}^2
\]

2. Area of the triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 9 \, \text{cm} \times 4 \, \text{cm} = 18 \, \text{cm}^2
\]

3. Shaded area:
\[
\text{Shaded area} = \text{Area}_{\text{rectangle}} - \text{Area}_{\text{triangle}} = 48 \, \text{cm}^2 - 18 \, \text{cm}^2 = 30 \, \text{cm}^2
\]

#### Final Answer for Part (d):
\[
\boxed{30}
\]

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Final Answers:

\[
\boxed{36, 803.5, 16.5, 30}
\]