Area of a Composite Figure worksheet with labeled shapes and dimensions.

To solve the problem of finding the area of each composite figure, we need to break down each figure into simpler shapes (such as rectangles, triangles, and trapezoids) and then calculate the area of each part. Finally, we sum up the areas of all the parts to get the total area of the composite figure.

Let's go through each figure step by step:

---

Figure 1:

The figure is a rectangle with a triangle cut out from one corner.

- Rectangle dimensions: \(20 \, \text{cm} \times 15 \, \text{cm}\)
- Triangle dimensions: Base = \(10 \, \text{cm}\), Height = \(10 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 20 \times 15 = 300 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 10 = 50 \, \text{cm}^2
\]

#### Step 3: Subtract the area of the triangle from the area of the rectangle.
\[
\text{Total area} = \text{Area of rectangle} - \text{Area of triangle} = 300 - 50 = 250 \, \text{cm}^2
\]

Answer for Figure 1:
\[
\boxed{250}
\]

---

Figure 2:

The figure is a combination of a rectangle and a triangle.

- Rectangle dimensions: \(20 \, \text{cm} \times 10 \, \text{cm}\)
- Triangle dimensions: Base = \(20 \, \text{cm}\), Height = \(10 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 20 \times 10 = 200 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 10 = 100 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the triangle.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 200 + 100 = 300 \, \text{cm}^2
\]

Answer for Figure 2:
\[
\boxed{300}
\]

---

Figure 3:

The figure is a combination of two rectangles.

- Rectangle 1 dimensions: \(8 \, \text{cm} \times 6 \, \text{cm}\)
- Rectangle 2 dimensions: \(4 \, \text{cm} \times 6 \, \text{cm}\)

#### Step 1: Calculate the area of Rectangle 1.
\[
\text{Area of Rectangle 1} = \text{length} \times \text{width} = 8 \times 6 = 48 \, \text{cm}^2
\]

#### Step 2: Calculate the area of Rectangle 2.
\[
\text{Area of Rectangle 2} = \text{length} \times \text{width} = 4 \times 6 = 24 \, \text{cm}^2
\]

#### Step 3: Add the areas of both rectangles.
\[
\text{Total area} = \text{Area of Rectangle 1} + \text{Area of Rectangle 2} = 48 + 24 = 72 \, \text{cm}^2
\]

Answer for Figure 3:
\[
\boxed{72}
\]

---

Figure 4:

The figure is a combination of a rectangle and a triangle.

- Rectangle dimensions: \(10 \, \text{cm} \times 5 \, \text{cm}\)
- Triangle dimensions: Base = \(5 \, \text{cm}\), Height = \(5 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 5 = 50 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 5 = 12.5 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the triangle.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 50 + 12.5 = 62.5 \, \text{cm}^2
\]

Answer for Figure 4:
\[
\boxed{62.5}
\]

---

Figure 5:

The figure is a combination of a rectangle and a triangle.

- Rectangle dimensions: \(15 \, \text{cm} \times 10 \, \text{cm}\)
- Triangle dimensions: Base = \(10 \, \text{cm}\), Height = \(5 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 15 \times 10 = 150 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 5 = 25 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the triangle.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 150 + 25 = 175 \, \text{cm}^2
\]

Answer for Figure 5:
\[
\boxed{175}
\]

---

Figure 6:

The figure is a combination of a rectangle and a triangle.

- Rectangle dimensions: \(12 \, \text{cm} \times 8 \, \text{cm}\)
- Triangle dimensions: Base = \(8 \, \text{cm}\), Height = \(4 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 12 \times 8 = 96 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 4 = 16 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the triangle.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 96 + 16 = 112 \, \text{cm}^2
\]

Answer for Figure 6:
\[
\boxed{112}
\]

---

Figure 7:

The figure is a combination of a rectangle and a triangle.

- Rectangle dimensions: \(20 \, \text{cm} \times 10 \, \text{cm}\)
- Triangle dimensions: Base = \(10 \, \text{cm}\), Height = \(10 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 20 \times 10 = 200 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 10 = 50 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the triangle.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 200 + 50 = 250 \, \text{cm}^2
\]

Answer for Figure 7:
\[
\boxed{250}
\]

---

Figure 8:

The figure is a combination of two rectangles.

- Rectangle 1 dimensions: \(10 \, \text{cm} \times 5 \, \text{cm}\)
- Rectangle 2 dimensions: \(5 \, \text{cm} \times 5 \, \text{cm}\)

#### Step 1: Calculate the area of Rectangle 1.
\[
\text{Area of Rectangle 1} = \text{length} \times \text{width} = 10 \times 5 = 50 \, \text{cm}^2
\]

#### Step 2: Calculate the area of Rectangle 2.
\[
\text{Area of Rectangle 2} = \text{length} \times \text{width} = 5 \times 5 = 25 \, \text{cm}^2
\]

#### Step 3: Add the areas of both rectangles.
\[
\text{Total area} = \text{Area of Rectangle 1} + \text{Area of Rectangle 2} = 50 + 25 = 75 \, \text{cm}^2
\]

Answer for Figure 8:
\[
\boxed{75}
\]

---

Figure 9:

The figure is a combination of a rectangle and a square.

- Rectangle dimensions: \(10 \, \text{cm} \times 5 \, \text{cm}\)
- Square dimensions: Side = \(5 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 5 = 50 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the square.
\[
\text{Area of square} = \text{side}^2 = 5 \times 5 = 25 \, \text{cm}^2
\]

#### Step 3: Add the area of the rectangle and the area of the square.
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of square} = 50 + 25 = 75 \, \text{cm}^2
\]

Answer for Figure 9:
\[
\boxed{75}
\]

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Final Answers:

\[
\boxed{250, 300, 72, 62.5, 175, 112, 250, 75, 75}
\]