Area of Compound Shapes worksheet with six geometric figures for calculating total area.

I'll solve this problem step by step, calculating the area of each shaded region in the compound shapes shown in the image.

Let me start by examining each shape one by one.

First, let's look at Shape 1:
This appears to be a parallelogram with a triangle cut out from it. I need to calculate the area of the parallelogram and subtract the area of the triangle.

Shape 2:
This looks like a circle with a trapezoid cut out from it. I'll need to calculate the area of the circle and subtract the area of the trapezoid.

Shape 3:
This is a square with a circle inside it. The shaded area is the square minus the circle.

Shape 4:
This appears to be a rectangle with two semicircles cut out from the bottom. I'll calculate the area of the rectangle and subtract the areas of the two semicircles (which together make one full circle).

Shape 5:
This is a triangle with a smaller rectangle cut out from it. I'll calculate the area of the triangle and subtract the area of the rectangle.

Shape 6:
This looks like a trapezoid with a semicircle cut out from the bottom. I'll calculate the area of the trapezoid and subtract the area of the semicircle.

Let me now calculate each one systematically.

Starting with Shape 1:
- Parallelogram: base = 8.7 cm, height = 4.9 cm
- Area of parallelogram = base × height = 8.7 × 4.9 = 42.63 cm²
- Triangle: base = 4.9 cm, height = 3.6 cm
- Area of triangle = (1/2) × base × height = (1/2) × 4.9 × 3.6 = 8.82 cm²
- Shaded area = 42.63 - 8.82 = 33.81 cm²

For Shape 2:
- Circle: diameter = 10.4 cm, so radius = 5.2 cm
- Area of circle = π × r² = 3.14 × 5.2² = 3.14 × 27.04 = 84.9056 cm²
- Trapezoid: bases = 7.8 cm and 4.6 cm, height = 3.8 cm
- Area of trapezoid = (1/2) × (base1 + base2) × height = (1/2) × (7.8 + 4.6) × 3.8 = (1/2) × 12.4 × 3.8 = 23.56 cm²
- Shaded area = 84.9056 - 23.56 = 61.3456 cm² ≈ 61.35 cm²

For Shape 3:
- Square: side = 10.2 cm
- Area of square = side² = 10.2² = 104.04 cm²
- Circle: diameter = 6.2 cm, so radius = 3.1 cm
- Area of circle = π × r² = 3.14 × 3.1² = 3.14 × 9.61 = 30.1754 cm²
- Shaded area = 104.04 - 30.1754 = 73.8646 cm² ≈ 73.86 cm²

For Shape 4:
- Rectangle: width = 12.5 cm, height = 7.3 cm
- Area of rectangle = width × height = 12.5 × 7.3 = 91.25 cm²
- Two semicircles: diameter = 6.5 cm each, so radius = 3.25 cm each
- Area of one semicircle = (1/2) × π × r² = (1/2) × 3.14 × 3.25² = (1/2) × 3.14 × 10.5625 = 16.58125 cm²
- Area of two semicircles = 2 × 16.58125 = 33.1625 cm²
- Shaded area = 91.25 - 33.1625 = 58.0875 cm² ≈ 58.09 cm²

For Shape 5:
- Triangle: base = 8.4 cm, height = 7.8 cm
- Area of triangle = (1/2) × base × height = (1/2) × 8.4 × 7.8 = 32.76 cm²
- Rectangle: width = 3.2 cm, height = 2.6 cm
- Area of rectangle = width × height = 3.2 × 2.6 = 8.32 cm²
- Shaded area = 32.76 - 8.32 = 24.44 cm²

For Shape 6:
- Trapezoid: bases = 11.6 cm and 8.2 cm, height = 6.8 cm
- Area of trapezoid = (1/2) × (base1 + base2) × height = (1/2) × (11.6 + 8.2) × 6.8 = (1/2) × 19.8 × 6.8 = 67.32 cm²
- Semicircle: diameter = 8.2 cm, so radius = 4.1 cm
- Area of semicircle = (1/2) × π × r² = (1/2) × 3.14 × 4.1² = (1/2) × 3.14 × 16.81 = 26.3897 cm²
- Shaded area = 67.32 - 26.3897 = 40.9303 cm² ≈ 40.93 cm²

Now I'll summarize all the answers:

1. Shape 1: 33.81 cm²
2. Shape 2: 61.35 cm²
3. Shape 3: 73.86 cm²
4. Shape 4: 58.09 cm²
5. Shape 5: 24.44 cm²
6. Shape 6: 40.93 cm²

These are the areas of the shaded regions for each compound shape, rounded to two decimal places as requested.