Area of Compound Shapes - Free Printable

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

Let's go through each shape step by step:

---

Shape 1:

- Description: A rectangle with a right triangle cut out.
- Dimensions:
- Rectangle: \(9 \, \text{cm} \times 4 \, \text{cm}\)
- Triangle: Base = \(5 \, \text{cm}\), Height = \(3 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 9 \times 4 = 36 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 3 = \frac{1}{2} \times 15 = 7.5 \, \text{cm}^2
\]

#### Step 3: Subtract the area of the triangle from the area of the rectangle.
\[
\text{Total area} = 36 - 7.5 = 28.5 \, \text{cm}^2
\]

Answer for Shape 1: \( \boxed{28.5} \)

---

Shape 2:

- Description: A trapezoid.
- Dimensions:
- Parallel sides: \(3 \, \text{cm}\) and \(6 \, \text{cm}\)
- Height: \(6 \, \text{cm}\)

#### Step 1: Use the formula for the area of a trapezoid.
\[
\text{Area of trapezoid} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times (3 + 6) \times 6 = \frac{1}{2} \times 9 \times 6 = \frac{1}{2} \times 54 = 27 \, \text{cm}^2
\]

Answer for Shape 2: \( \boxed{27} \)

---

Shape 3:

- Description: A combination of a rectangle and a trapezoid.
- Dimensions:
- Rectangle: \(8 \, \text{cm} \times 3 \, \text{cm}\)
- Trapezoid: Parallel sides = \(3 \, \text{cm}\) and \(1 \, \text{cm}\), Height = \(6 - 3 = 3 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 8 \times 3 = 24 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the trapezoid.
\[
\text{Area of trapezoid} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}
\]
\[
\text{Area} = \frac{1}{2} \times (3 + 1) \times 3 = \frac{1}{2} \times 4 \times 3 = \frac{1}{2} \times 12 = 6 \, \text{cm}^2
\]

#### Step 3: Add the areas of the rectangle and the trapezoid.
\[
\text{Total area} = 24 + 6 = 30 \, \text{cm}^2
\]

Answer for Shape 3: \( \boxed{30} \)

---

Shape 4:

- Description: A combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(4 \, \text{cm} \times 4 \, \text{cm}\)
- Triangle: Base = \(4 \, \text{cm}\), Height = \(4 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 4 \times 4 = 16 \, \text{cm}^2
\]

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

#### Step 3: Add the areas of the rectangle and the triangle.
\[
\text{Total area} = 16 + 8 = 24 \, \text{cm}^2
\]

Answer for Shape 4: \( \boxed{24} \)

---

Shape 5:

- Description: A combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(10 \, \text{cm} \times 4 \, \text{cm}\)
- Triangle: Base = \(10 \, \text{cm}\), Height = \(4 - 3 = 1 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 4 = 40 \, \text{cm}^2
\]

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

#### Step 3: Subtract the area of the triangle from the area of the rectangle.
\[
\text{Total area} = 40 - 5 = 35 \, \text{cm}^2
\]

Answer for Shape 5: \( \boxed{35} \)

---

Shape 6:

- Description: A combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(10 \, \text{cm} \times 4 \, \text{cm}\)
- Triangle: Base = \(10 \, \text{cm}\), Height = \(6 - 4 = 2 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 4 = 40 \, \text{cm}^2
\]

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

#### Step 3: Add the areas of the rectangle and the triangle.
\[
\text{Total area} = 40 + 10 = 50 \, \text{cm}^2
\]

Answer for Shape 6: \( \boxed{50} \)

---

Shape 7:

- Description: A combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(12 \, \text{cm} \times 4 \, \text{cm}\)
- Triangle: Base = \(12 \, \text{cm}\), Height = \(4 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 12 \times 4 = 48 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 4 = \frac{1}{2} \times 48 = 24 \, \text{cm}^2
\]

#### Step 3: Add the areas of the rectangle and the triangle.
\[
\text{Total area} = 48 + 24 = 72 \, \text{cm}^2
\]

Answer for Shape 7: \( \boxed{72} \)

---

Shape 8:

- Description: A combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(18 \, \text{cm} \times 6 \, \text{cm}\)
- Triangle: Base = \(18 \, \text{cm}\), Height = \(8 - 6 = 2 \, \text{cm}\)

#### Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 18 \times 6 = 108 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 \times 2 = \frac{1}{2} \times 36 = 18 \, \text{cm}^2
\]

#### Step 3: Add the areas of the rectangle and the triangle.
\[
\text{Total area} = 108 + 18 = 126 \, \text{cm}^2
\]

Answer for Shape 8: \( \boxed{126} \)

---

Shape 9:

- Description: A combination of a rectangle and a parallelogram.
- Dimensions:
- Rectangle: \(6 \, \text{cm} \times 8 \, \text{cm}\)
- Parallelogram: Base = \(5 \, \text{cm}\), Height = \(8 \, \text{cm}\)

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

#### Step 2: Calculate the area of the parallelogram.
\[
\text{Area of parallelogram} = \text{base} \times \text{height} = 5 \times 8 = 40 \, \text{cm}^2
\]

#### Step 3: Add the areas of the rectangle and the parallelogram.
\[
\text{Total area} = 48 + 40 = 88 \, \text{cm}^2
\]

Answer for Shape 9: \( \boxed{88} \)

---

Final Answers:

1. \( \boxed{28.5} \)
2. \( \boxed{27} \)
3. \( \boxed{30} \)
4. \( \boxed{24} \)
5. \( \boxed{35} \)
6. \( \boxed{50} \)
7. \( \boxed{72} \)
8. \( \boxed{126} \)
9. \( \boxed{88} \)