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

I'll solve each compound shape problem step by step, finding the area of each one.

Problem 1: Rectangle with semicircle on top
- Rectangle: width = 11 cm, height = 5 cm
- Semicircle diameter = 11 cm, so radius = 5.5 cm
- Rectangle area = 11 × 5 = 55 cm²
- Semicircle area = (π × 5.5²)/2 = (3.14 × 30.25)/2 = 94.985/2 = 47.49 cm²
- Total = 55 + 47.49 = 102.49 cm²

Let me recalculate more carefully:
- Rectangle: 11 × 5 = 55 cm²
- Semicircle: πr²/2 where r = 11/2 = 5.5
- Semicircle = (3.14 × 5.5²)/2 = (3.14 × 30.25)/2 = 47.4925 cm²
- Total = 55 + 47.4925 ≈ 102.5 cm²

Problem 2: Trapezoid
- Top base = 12 cm, bottom base = 20 cm, height = 8 cm
- Area = (1/2)(b₁ + b₂)h = (1/2)(12 + 20)(8) = (1/2)(32)(8) = 16 × 8 = 128 cm²

Problem 3: Hexagon made of triangles
- This appears to be a regular hexagon with side length 8 cm
- A regular hexagon can be divided into 6 equilateral triangles
- Area of one equilateral triangle = (√3/4)s² = (1.732/4)(8²) = 0.433 × 64 = 27.712 cm²
- Total area = 6 × 27.712 = 166.27 cm²

Wait, let me check if this is showing the apothem or something else. Looking at the diagram, it shows 8 cm as the distance from center to vertex (radius). For a regular hexagon:
- Area = (3√3/2)r² where r is the radius
- Area = (3 × 1.732/2)(8²) = 2.598 × 64 = 166.3 cm²

Problem 4: L-shaped figure
- Can split into two rectangles:
- Bottom rectangle: 20 × 8 = 160 cm²
- Top rectangle: 12 × 10 = 120 cm² (since total height is 18, and bottom is 8)
- Wait, let me reconsider. The figure shows:
- Left side: 18 cm total height
- Bottom: 20 cm width
- Right vertical part: 8 cm
- Top horizontal: 12 cm

Split method 1:
- Large rectangle minus cutout: 20 × 18 - 8 × 10 = 360 - 80 = 280 cm²

Split method 2:
- Left rectangle: 12 × 18 = 216 cm²
- Right rectangle: 8 × 8 = 64 cm²
- Total = 216 + 64 = 280 cm²

Answer: 280 cm²

Problem 5: Parallelogram with triangle on top
- Parallelogram: base = 14 cm, height = 10 cm
- Triangle: base = 14 cm, height = 6 cm
- Parallelogram area = 14 × 10 = 140 cm²
- Triangle area = (1/2)(14)(6) = 42 cm²
- Total = 140 + 42 = 182 cm²

Problem 6: Semicircle with triangle inside
- Diameter = 10 cm, so radius = 5 cm
- Triangle height = 4 cm
- Semicircle area = (π × 5²)/2 = (3.14 × 25)/2 = 39.25 cm²
- Triangle area = (1/2)(10)(4) = 20 cm²
- Shaded area = 39.25 - 20 = 19.3 cm²

Final Answer:
1) 102.5 cm²
2) 128 cm²
3) 166.3 cm²
4) 280 cm²
5) 182 cm²
6) 19.3 cm²