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

Looking at the worksheet, I need to find the area of each shaded compound shape. The instructions say to round answers to 2 decimal places and use π = 3.14.

Let me go through each shape one by one:

Shape 1 (Top Left):
This is a rectangle with two half-circles on the sides (making one full circle) and a semicircle on top.
- Rectangle: 8 cm × 4 cm = 32 cm²
- Circle (from two half-circles): radius = 2 cm → Area = πr² = 3.14 × 2² = 12.56 cm²
- Semicircle on top: radius = 2 cm → Area = ½ × πr² = ½ × 12.56 = 6.28 cm²
Total = 32 + 12.56 + 6.28 = 50.84 cm²

Wait — looking again, the semicircle on top has diameter 8 cm, so radius = 4 cm.
Semicircle area = ½ × π × 4² = ½ × 3.14 × 16 = 25.12 cm²
Circle from sides: radius = 2 cm → 3.14 × 4 = 12.56 cm²
Rectangle: 8 × 4 = 32 cm²
Total = 32 + 12.56 + 25.12 = 69.68 cm²

Actually, let me re-examine the diagram. The shape looks like a rectangle with two half-circles on the left and right (forming a full circle), and a semicircle on top. But the dimensions show:
- Overall height: 4 cm
- Width: 8 cm
- The semicircle on top spans the full 8 cm width → radius = 4 cm
- The side half-circles have diameter = 4 cm → radius = 2 cm

So:
Rectangle: 8 × 4 = 32 cm²
Full circle from sides: π × 2² = 12.56 cm²
Semicircle on top: ½ × π × 4² = 25.12 cm²
Total = 32 + 12.56 + 25.12 = 69.68 cm²

Shape 2 (Top Right):
This is a square with two semicircles cut out from top and bottom.
- Square: 10 cm × 10 cm = 100 cm²
- Two semicircles make one full circle: diameter = 10 cm → radius = 5 cm
- Circle area: π × 5² = 3.14 × 25 = 78.5 cm²
Shaded area = 100 - 78.5 = 21.50 cm²

Shape 3 (Middle Left):
This is a trapezoid with a square hole in the middle.
- Trapezoid: bases 10 cm and 12 cm, height 8 cm
Area = ½ × (10 + 12) × 8 = ½ × 22 × 8 = 88 cm²
- Square hole: 4 cm × 4 cm = 16 cm²
Shaded area = 88 - 16 = 72.00 cm²

Shape 4 (Middle Right):
This is a parallelogram with a triangle cut out from the right side.
- Parallelogram: base = 10 cm, height = 6 cm → Area = 10 × 6 = 60 cm²
- Triangle cut out: base = 4 cm, height = 6 cm → Area = ½ × 4 × 6 = 12 cm²
Shaded area = 60 - 12 = 48.00 cm²

Wait, looking more carefully — it might be a trapezoid. Let me check the dimensions:
Top base = 6 cm, bottom base = 10 cm, height = 6 cm
Trapezoid area = ½ × (6 + 10) × 6 = ½ × 16 × 6 = 48 cm²
That matches. So shaded area = 48.00 cm²

Shape 5 (Bottom Left):
This is a parallelogram with a semicircle cut out from the right side.
- Parallelogram: base = 10 cm, height = 8 cm → Area = 10 × 8 = 80 cm²
- Semicircle cut out: diameter = 8 cm → radius = 4 cm
- Semicircle area = ½ × π × 4² = ½ × 3.14 × 16 = 25.12 cm²
Shaded area = 80 - 25.12 = 54.88 cm²

Shape 6 (Bottom Right):
This is a rectangle with a triangle attached to the right side.
- Rectangle: 10 cm × 6 cm = 60 cm²
- Triangle: base = 6 cm, height = 5 cm → Area = ½ × 6 × 5 = 15 cm²
Total area = 60 + 15 = 75.00 cm²

Let me double-check Shape 6:
The rectangle is 10 cm long and 6 cm high.
The triangle has base 6 cm (same as rectangle height) and height 5 cm (extending to the right).
Yes, that's correct.

Now let me summarize all answers:

1. 69.68 cm²
2. 21.50 cm²
3. 72.00 cm²
4. 48.00 cm²
5. 54.88 cm²
6. 75.00 cm²

Final Answer:
1. 69.68 cm²
2. 21.50 cm²
3. 72.00 cm²
4. 48.00 cm²
5. 54.88 cm²
6. 75.00 cm²