Area of Complex Figures Worksheet
Calculate the area of various complex geometric figures by decomposing them into simpler shapes. Includes composite figures, shaded regions, and real-world applications.
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Area of Complex Figures
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Read each question carefully and calculate the area of the complex figures. Show all your work.
1. Find the area of the figure below, which consists of a rectangle and a semicircle. Use π ≈ 3.14.
Show your work:
Area:
2. Calculate the area of the shaded region. The outer rectangle has dimensions 10 ft by 7 ft, and the inner square has a side length of 4 ft.
Show your work:
Area of shaded region:
3. A floor plan is shown below. All angles are right angles. Find the total area of the floor.
Show your work:
Total Area:
4. Which of the following formulas would you use to find the area of a figure composed of a triangle and a rectangle?
A = (l × w) + (0.5 × b × h)
A = (l + w) × (b + h)
A = (l × w) - (0.5 × b × h)
A = (2l + 2w) + (b + h + s)
5. To find the area of a complex figure, you can often it into simpler geometric shapes like rectangles, triangles, and circles.
6. The area of a figure is the amount of it covers.
7. Describe a real-world scenario where you would need to calculate the area of a complex figure. Explain why it's a complex figure and how you would approach finding its area.