Area and Perimeter of Composite Shapes Concept CW worksheet | Live ... - Free Printable

To solve the problem of finding the area of the shaded regions in each figure, we will break down each composite shape into simpler geometric shapes (rectangles, triangles, circles, etc.) and calculate their areas step by step. Let's go through each figure one by one.

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Figure 1:

The shaded region consists of a rectangle and a semicircle.

- Rectangle:
- Length = 12 yd
- Width = 4 yd
- Area of rectangle = \( \text{Length} \times \text{Width} = 12 \times 4 = 48 \) square yards

- Semicircle:
- Diameter = 8 yd
- Radius = \( \frac{8}{2} = 4 \) yd
- Area of full circle = \( \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \) square yards
- Area of semicircle = \( \frac{1}{2} \times 50.24 = 25.12 \) square yards

- Total Area:
- Total shaded area = Area of rectangle + Area of semicircle
- Total shaded area = \( 48 + 25.12 = 73.12 \) square yards

Answer for Figure 1:
\[ \boxed{73.12} \]

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Figure 2:

The shaded region is a combination of a triangle and a semicircle.

- Triangle:
- Base = 11 in
- Height = 10 in
- Area of triangle = \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 11 \times 10 = 55 \) square inches

- Semicircle:
- Diameter = 11 in
- Radius = \( \frac{11}{2} = 5.5 \) in
- Area of full circle = \( \pi r^2 = 3.14 \times 5.5^2 = 3.14 \times 30.25 = 94.985 \) square inches
- Area of semicircle = \( \frac{1}{2} \times 94.985 = 47.4925 \) square inches

- Total Area:
- Total shaded area = Area of triangle + Area of semicircle
- Total shaded area = \( 55 + 47.4925 = 102.4925 \approx 102.49 \) square inches

Answer for Figure 2:
\[ \boxed{102.49} \]

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Figure 3:

The shaded region is a combination of a triangle and a rectangle.

- Triangle:
- Base = 12 ft
- Height = 2 ft
- Area of triangle = \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 \times 2 = 12 \) square feet

- Rectangle:
- Length = 6 ft
- Width = 6 ft
- Area of rectangle = \( \text{Length} \times \text{Width} = 6 \times 6 = 36 \) square feet

- Total Area:
- Total shaded area = Area of triangle + Area of rectangle
- Total shaded area = \( 12 + 36 = 48 \) square feet

Answer for Figure 3:
\[ \boxed{48.00} \]

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Figure 4:

The shaded region is a large rectangle with a smaller rectangle removed from it.

- Large Rectangle:
- Length = 10 yd
- Width = 9 yd
- Area of large rectangle = \( \text{Length} \times \text{Width} = 10 \times 9 = 90 \) square yards

- Small Rectangle:
- Length = 4 yd
- Width = 3 yd
- Area of small rectangle = \( \text{Length} \times \text{Width} = 4 \times 3 = 12 \) square yards

- Total Area:
- Total shaded area = Area of large rectangle - Area of small rectangle
- Total shaded area = \( 90 - 12 = 78 \) square yards

Answer for Figure 4:
\[ \boxed{78.00} \]

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Figure 5:

The shaded region is a large rectangle with two smaller rectangles removed from it.

- Large Rectangle:
- Length = 12 in
- Width = 10 in
- Area of large rectangle = \( \text{Length} \times \text{Width} = 12 \times 10 = 120 \) square inches

- Smaller Rectangles:
- First smaller rectangle:
- Length = 5 in
- Width = 5 in
- Area = \( 5 \times 5 = 25 \) square inches
- Second smaller rectangle:
- Length = 5 in
- Width = 5 in
- Area = \( 5 \times 5 = 25 \) square inches

- Total Area:
- Total shaded area = Area of large rectangle - (Area of first smaller rectangle + Area of second smaller rectangle)
- Total shaded area = \( 120 - (25 + 25) = 120 - 50 = 70 \) square inches

Answer for Figure 5:
\[ \boxed{70.00} \]

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Figure 6:

The shaded region is a trapezoid.

- Trapezoid:
- Bases = 6 ft and 9 ft
- Height = 14 ft
- Area of trapezoid = \( \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \)
- Area of trapezoid = \( \frac{1}{2} \times (6 + 9) \times 14 = \frac{1}{2} \times 15 \times 14 = 105 \) square feet

Answer for Figure 6:
\[ \boxed{105.00} \]

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Final Answers:

1. \( \boxed{73.12} \)
2. \( \boxed{102.49} \)
3. \( \boxed{48.00} \)
4. \( \boxed{78.00} \)
5. \( \boxed{70.00} \)
6. \( \boxed{105.00} \)