Area of Compound Shapes (Composite Shapes) Worksheets - Free Printable

To solve the problem of finding the area of each compound shape, we need to break down each shape into simpler geometric figures (such as rectangles, triangles, circles, etc.) and then calculate their areas individually. Finally, we combine these areas according to whether they are added or subtracted based on the structure of the compound shape.

Let's go through each part step by step:

---

Part A:

The shape consists of a rectangle with a semicircle cut out from one side.

#### Step 1: Identify the dimensions
- The rectangle has a length of \( 8 \, \text{cm} \) and a width of \( 4 \, \text{cm} \).
- The diameter of the semicircle is equal to the width of the rectangle, which is \( 4 \, \text{cm} \). Therefore, the radius \( r \) of the semicircle is:
\[
r = \frac{4}{2} = 2 \, \text{cm}
\]

#### Step 2: Calculate the area of the rectangle
The area \( A_{\text{rectangle}} \) of the rectangle is:
\[
A_{\text{rectangle}} = \text{length} \times \text{width} = 8 \times 4 = 32 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the semicircle
The area \( A_{\text{semicircle}} \) of a semicircle is half the area of a full circle. The formula for the area of a full circle is \( \pi r^2 \), so the area of the semicircle is:
\[
A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \cdot 4 = 2\pi \, \text{cm}^2
\]
Using \( \pi \approx 3.14 \):
\[
A_{\text{semicircle}} \approx 2 \times 3.14 = 6.28 \, \text{cm}^2
\]

#### Step 4: Subtract the area of the semicircle from the area of the rectangle
The total area \( A_{\text{total}} \) of the compound shape is:
\[
A_{\text{total}} = A_{\text{rectangle}} - A_{\text{semicircle}} = 32 - 6.28 = 25.72 \, \text{cm}^2
\]

#### Final Answer for Part A:
\[
\boxed{25.72}
\]

---

Part B:

The shape consists of a rectangle with a triangular cutout.

#### Step 1: Identify the dimensions
- The rectangle has a length of \( 10 \, \text{cm} \) and a width of \( 6 \, \text{cm} \).
- The triangular cutout has a base of \( 6 \, \text{cm} \) (same as the width of the rectangle) and a height of \( 3 \, \text{cm} \).

#### Step 2: Calculate the area of the rectangle
The area \( A_{\text{rectangle}} \) of the rectangle is:
\[
A_{\text{rectangle}} = \text{length} \times \text{width} = 10 \times 6 = 60 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the triangle
The area \( A_{\text{triangle}} \) of a triangle is given by:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 = 9 \, \text{cm}^2
\]

#### Step 4: Subtract the area of the triangle from the area of the rectangle
The total area \( A_{\text{total}} \) of the compound shape is:
\[
A_{\text{total}} = A_{\text{rectangle}} - A_{\text{triangle}} = 60 - 9 = 51 \, \text{cm}^2
\]

#### Final Answer for Part B:
\[
\boxed{51}
\]

---

Part C:

The shape consists of a square with a circular cutout.

#### Step 1: Identify the dimensions
- The side length of the square is \( 7 \, \text{cm} \).
- The diameter of the circle is \( 3.5 \, \text{cm} \). Therefore, the radius \( r \) of the circle is:
\[
r = \frac{3.5}{2} = 1.75 \, \text{cm}
\]

#### Step 2: Calculate the area of the square
The area \( A_{\text{square}} \) of the square is:
\[
A_{\text{square}} = \text{side}^2 = 7^2 = 49 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the circle
The area \( A_{\text{circle}} \) of the circle is:
\[
A_{\text{circle}} = \pi r^2 = \pi (1.75)^2 = \pi \cdot 3.0625
\]
Using \( \pi \approx 3.14 \):
\[
A_{\text{circle}} \approx 3.14 \cdot 3.0625 = 9.62 \, \text{cm}^2
\]

#### Step 4: Subtract the area of the circle from the area of the square
The total area \( A_{\text{total}} \) of the compound shape is:
\[
A_{\text{total}} = A_{\text{square}} - A_{\text{circle}} = 49 - 9.62 = 39.38 \, \text{cm}^2
\]

#### Final Answer for Part C:
\[
\boxed{39.38}
\]

---

Part D:

The shape consists of a large square with a smaller square cut out from one corner.

#### Step 1: Identify the dimensions
- The side length of the large square is \( 10 \, \text{cm} \).
- The side length of the smaller square is \( 4 \, \text{cm} \).

#### Step 2: Calculate the area of the large square
The area \( A_{\text{large square}} \) of the large square is:
\[
A_{\text{large square}} = \text{side}^2 = 10^2 = 100 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the smaller square
The area \( A_{\text{small square}} \) of the smaller square is:
\[
A_{\text{small square}} = \text{side}^2 = 4^2 = 16 \, \text{cm}^2
\]

#### Step 4: Subtract the area of the smaller square from the area of the large square
The total area \( A_{\text{total}} \) of the compound shape is:
\[
A_{\text{total}} = A_{\text{large square}} - A_{\text{small square}} = 100 - 16 = 84 \, \text{cm}^2
\]

#### Final Answer for Part D:
\[
\boxed{84}
\]

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Final Answers:

\[
\boxed{25.72, 51, 39.38, 84}
\]