Area of Compound Shapes 1 - Free Printable

Problem: Find the area of each compound shape. Round the answer to 2 decimal places if necessary.

#### Shape 1:
The shape consists of a rectangle and a semicircle on top.

- Given dimensions:
- Rectangle:
- Width = 8 ft
- Height = 12 ft
- Semicircle:
- Diameter = 8 ft (same as the width of the rectangle)
- Radius = \( \frac{8}{2} = 4 \) ft

- Area of the rectangle:
\[
\text{Area}_{\text{rectangle}} = \text{width} \times \text{height} = 8 \times 12 = 96 \, \text{ft}^2
\]

- Area of the semicircle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \cdot 16 = 8\pi \, \text{ft}^2
\]
Using \( \pi \approx 3.14 \):
\[
\text{Area}_{\text{semicircle}} \approx 8 \times 3.14 = 25.12 \, \text{ft}^2
\]

- Total area of the shape:
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 96 + 25.12 = 121.12 \, \text{ft}^2
\]

Answer for Shape 1:
\[
\boxed{121.12}
\]

---

#### Shape 2:
The shape is a combination of a rectangle and a triangle.

- Given dimensions:
- Rectangle:
- Length = 13 in
- Width = 8 in
- Triangle:
- Base = 19 in - 13 in = 6 in
- Height = 8 in (same as the height of the rectangle)

- Area of the rectangle:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 13 \times 8 = 104 \, \text{in}^2
\]

- Area of the triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24 \, \text{in}^2
\]

- Total area of the shape:
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 104 + 24 = 128 \, \text{in}^2
\]

Answer for Shape 2:
\[
\boxed{128}
\]

---

#### Shape 3:
The shape is a rectangle with a smaller rectangle cut out from it.

- Given dimensions:
- Larger rectangle:
- Length = 11 cm
- Width = 4 cm
- Smaller rectangle (cut-out):
- Length = 4 cm
- Width = 2 cm

- Area of the larger rectangle:
\[
\text{Area}_{\text{larger}} = \text{length} \times \text{width} = 11 \times 4 = 44 \, \text{cm}^2
\]

- Area of the smaller rectangle:
\[
\text{Area}_{\text{smaller}} = \text{length} \times \text{width} = 4 \times 2 = 8 \, \text{cm}^2
\]

- Total area of the shape:
\[
\text{Total Area} = \text{Area}_{\text{larger}} - \text{Area}_{\text{smaller}} = 44 - 8 = 36 \, \text{cm}^2
\]

Answer for Shape 3:
\[
\boxed{36}
\]

---

#### Shape 4:
The shape is a triangle.

- Given dimensions:
- Base = 6 ft
- Height = 7 ft

- Area of the triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 7 = 21 \, \text{ft}^2
\]

Answer for Shape 4:
\[
\boxed{21}
\]

---

Final Answers:

1. \(\boxed{121.12}\)
2. \(\boxed{128}\)
3. \(\boxed{36}\)
4. \(\boxed{21}\)