Perimeter with a Semicircle Attached to a Rectangle

🔑 Key Concepts

  • Perimeter is the total distance around the outside of a figure.
  • Curved edges contribute part of a circle’s circumference.
  • A semicircle contributes half of a circle’s circumference.
  • An interior line is not included in the perimeter.
  • Add all exposed straight sides and curved distances.

💡 Main Idea

To find the perimeter of a rectangle with a semicircle attached, add the three exposed sides of the rectangle and the curved semicircular arc. Do not include the diameter separating the rectangle and semicircle because it lies inside the composite figure.

✏️ Worked Example — Perimeter with a Semicircular Edge

🧠 Math Vocabulary

  • Perimeter: The total distance around the outside of a figure.
  • Circumference: The distance around a full circle.
  • Semicircle: Half of a circle.
  • Diameter: The distance across a circle through its center.
  • Radius: The distance from the center to the circle; it is half the diameter.
  • Composite figure: A figure formed by combining two or more simpler shapes.
  • Semicircular arc: The curved edge of a semicircle, with length \(\pi r\) or \(\frac{\pi d}{2}\).

📚 What You Should Already Know

Students should know how to add side lengths to find perimeter, identify exposed and interior edges, distinguish radius from diameter, and use \(C=\pi d\) or \(C=2\pi r\) to find circumference.

🚀 What Comes Next

Students will solve more complex perimeter problems involving multiple semicircles, quarter circles, irregular figures, and composite shapes that combine several straight and curved edges.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform.