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

I will solve the problem in the image, which is to find the area of each shaded composite figure and round the answer to two decimal places using 3.14 for π.

I'll tackle each figure one by one, breaking them down into simpler shapes whose areas I can calculate.

Figure 1

This figure looks like a rectangle attached to a semicircle.

- Rectangle: The dimensions are 6 units (width) by 3 units (height).
- Area = width × height = 6 × 3 = 18 square units.
- Semicircle: The diameter is 3 units (same as the height of the rectangle), so the radius is 1.5 units.
- Area of a full circle = π × r² = 3.14 × (1.5)² = 3.14 × 2.25 = 7.065 square units.
- Area of the semicircle = 7.065 / 2 = 3.5325 square units.
- Total Area: 18 + 3.5325 = 21.5325 square units.
- Rounded to two decimal places: 21.53 square units.

Figure 2

This figure is a triangle with a semicircle on top.

- Triangle: The base is 6 units and the height is 5 units.
- Area = (base × height) / 2 = (6 × 5) / 2 = 15 square units.
- Semicircle: The diameter is 6 units (same as the base of the triangle), so the radius is 3 units.
- Area of a full circle = π × r² = 3.14 × (3)² = 3.14 × 9 = 28.26 square units.
- Area of the semicircle = 28.26 / 2 = 14.13 square units.
- Total Area: 15 + 14.13 = 29.13 square units.
- Rounded to two decimal places: 29.13 square units.

Figure 3

This figure is an arrow shape, which can be seen as a rectangle with two triangles on the sides.

- Central Rectangle: The width is 4 units and the height is 3 units.
- Area = width × height = 4 × 3 = 12 square units.
- Two Side Triangles: Each triangle has a base of 2 units (the total width is 8, so the extra on each side is (8-4)/2 = 2) and a height of 3 units.
- Area of one triangle = (base × height) / 2 = (2 × 3) / 2 = 3 square units.
- Area of two triangles = 3 × 2 = 6 square units.
- Total Area: 12 + 6 = 18 square units.
- Rounded to two decimal places: 18.00 square units.

Figure 4

This figure is a rectangle with a smaller rectangle cut out from the top.

- Outer Rectangle: The width is 8 units and the height is 6 units.
- Area = width × height = 8 × 6 = 48 square units.
- Inner Rectangle (cut out): The width is 4 units and the height is 2 units.
- Area = width × height = 4 × 2 = 8 square units.
- Shaded Area: 48 - 8 = 40 square units.
- Rounded to two decimal places: 40.00 square units.

Figure 5

This figure is a rectangle with a semicircle cut out from the bottom.

- Rectangle: The width is 8 units and the height is 6 units.
- Area = width × height = 8 × 6 = 48 square units.
- Semicircle (cut out): The diameter is 8 units (same as the width of the rectangle), so the radius is 4 units.
- Area of a full circle = π × r² = 3.14 × (4)² = 3.14 × 16 = 50.24 square units.
- Area of the semicircle = 50.24 / 2 = 25.12 square units.
- Shaded Area: 48 - 25.12 = 22.88 square units.
- Rounded to two decimal places: 22.88 square units.

Figure 6

This figure is a rectangle with a triangle on top.

- Rectangle: The width is 6 units and the height is 5 units.
- Area = width × height = 6 × 5 = 30 square units.
- Triangle: The base is 6 units (same as the width of the rectangle) and the height is 4 units.
- Area = (base × height) / 2 = (6 × 4) / 2 = 12 square units.
- Total Area: 30 + 12 = 42 square units.
- Rounded to two decimal places: 42.00 square units.

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Here are the final answers for each figure:

1. 21.53
2. 29.13
3. 18.00
4. 40.00
5. 22.88
6. 42.00