Area of Composite Figures with Semicircles

🔑 Key Concepts

  • The center square has a side length of \(16\) units.
  • Each side of the square is also the diameter of one semicircle.
  • Each semicircle has a radius of \(8\) units.
  • Four semicircles combine to form two complete circles.
  • Find the square’s area and the area of two circles, then add them.

💡 Main Idea

The composite figure consists of a square and four semicircles. Since each semicircle has a diameter equal to the square’s \(16\)-unit side, each radius is \(8\) units. The four semicircles can be paired to create two complete circles. Find the area of the square, find the combined area of the two circles, and add the results to determine the total area.

✏️ Worked Example

🧠 Math Vocabulary

  • Composite figure: A figure made by combining two or more basic geometric shapes.
  • Square: A quadrilateral with four congruent sides and four right angles.
  • Semicircle: Half of a circle.
  • Diameter: A segment passing through a circle’s center with endpoints on the circle.
  • Radius: A segment from a circle’s center to a point on the circle; it is half the diameter.
  • Area: The amount of two-dimensional space inside a figure, measured in square units.
  • Decompose: To separate a composite figure into simpler shapes.
  • Approximate: To find a value close to the exact value, often by rounding.

📚 What You Should Already Know

You should know how to find the area of a square using \(A=s^2\) and the area of a circle using \(A=\pi r^2\). You should also understand that the radius is half the diameter and that two semicircles combine to form one complete circle.

🚀 What Comes Next

Next, you can find the areas of more complex composite figures involving rectangles, triangles, trapezoids, parallelograms, circles, semicircles, and shaded regions. Some problems may require adding several pieces, subtracting missing sections, or determining an unmarked dimension first.

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