Area of Shaded Regions. Interactive worksheet | TopWorksheets - Free Printable

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

---

(a)

The image shows a square with a smaller rectangle inside it. The dimensions are as follows:
- The outer square has a side length of 15 cm.
- The inner rectangle has dimensions 9 cm (width) and 3 cm (height).

#### Step 1: Calculate the area of the outer square
The formula for the area of a square is:
\[
\text{Area of square} = \text{side}^2
\]
\[
\text{Area of outer square} = 15 \times 15 = 225 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the inner rectangle
The formula for the area of a rectangle is:
\[
\text{Area of rectangle} = \text{length} \times \text{width}
\]
\[
\text{Area of inner rectangle} = 9 \times 3 = 27 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the shaded region
The shaded region is the area of the outer square minus the area of the inner rectangle:
\[
\text{Area of shaded region} = \text{Area of outer square} - \text{Area of inner rectangle}
\]
\[
\text{Area of shaded region} = 225 - 27 = 198 \, \text{cm}^2
\]

Answer for (a):
\[
\boxed{198}
\]

---

(b)

The image shows a larger square with a smaller square inside it. The dimensions are as follows:
- The outer square has a side length of 40 cm.
- The inner square has a side length of 6 cm.

#### Step 1: Calculate the area of the outer square
\[
\text{Area of outer square} = 40 \times 40 = 1600 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the inner square
\[
\text{Area of inner square} = 6 \times 6 = 36 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the shaded region
The shaded region is the area of the outer square minus the area of the inner square:
\[
\text{Area of shaded region} = \text{Area of outer square} - \text{Area of inner square}
\]
\[
\text{Area of shaded region} = 1600 - 36 = 1564 \, \text{cm}^2
\]

Answer for (b):
\[
\boxed{1564}
\]

---

(c)

The image shows a triangle with a smaller triangle cut out from it. The dimensions are as follows:
- The outer triangle has a base of 10 cm and a height of 6 cm.
- The inner triangle has a base of 4 cm and a height of 3 cm.

#### Step 1: Calculate the area of the outer triangle
The formula for the area of a triangle is:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area of outer triangle} = \frac{1}{2} \times 10 \times 6 = 30 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the inner triangle
\[
\text{Area of inner triangle} = \frac{1}{2} \times 4 \times 3 = 6 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the shaded region
The shaded region is the area of the outer triangle minus the area of the inner triangle:
\[
\text{Area of shaded region} = \text{Area of outer triangle} - \text{Area of inner triangle}
\]
\[
\text{Area of shaded region} = 30 - 6 = 24 \, \text{cm}^2
\]

Answer for (c):
\[
\boxed{24}
\]

---

(d)

The image shows a large triangle divided into three smaller triangles. The dimensions are as follows:
- The large triangle has a base of 20 m and a height of 12 m.
- The shaded region consists of two smaller triangles with bases of 10 m and heights of 6 m each.

#### Step 1: Calculate the area of the large triangle
\[
\text{Area of large triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
\text{Area of large triangle} = \frac{1}{2} \times 20 \times 12 = 120 \, \text{m}^2
\]

#### Step 2: Calculate the area of one of the smaller unshaded triangles
Each unshaded triangle has a base of 10 m and a height of 6 m:
\[
\text{Area of one unshaded triangle} = \frac{1}{2} \times 10 \times 6 = 30 \, \text{m}^2
\]

#### Step 3: Calculate the total area of the two unshaded triangles
\[
\text{Total area of unshaded triangles} = 30 + 30 = 60 \, \text{m}^2
\]

#### Step 4: Calculate the area of the shaded region
The shaded region is the area of the large triangle minus the total area of the two unshaded triangles:
\[
\text{Area of shaded region} = \text{Area of large triangle} - \text{Total area of unshaded triangles}
\]
\[
\text{Area of shaded region} = 120 - 60 = 60 \, \text{m}^2
\]

Answer for (d):
\[
\boxed{60}
\]

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Final Answers:

\[
\boxed{198, 1564, 24, 60}
\]