📝 Practice Worksheets
🔑 Key Concepts
- Perimeter is the total distance around the outside of a figure.
- Curved edges contribute part of a circle’s circumference.
- Each semicircular arc is half of a full circumference.
- Two semicircular arcs with the same diameter combine to form one full circumference.
- Only exposed straight and curved edges are included in the perimeter.
💡 Main Idea
When a figure contains two semicircular arcs with the same diameter, the two curved distances combine to equal the circumference of one complete circle. Find that circumference, then add the lengths of the exposed straight sides to determine the total perimeter.
🧠 Vocabulary and Equations
- Perimeter: The total distance around the outside of a figure.
- Circumference: The distance around a circle.
- Radius: The distance from the center of a circle to its edge.
- Diameter: The distance across a circle through its center; the diameter is twice the radius.
- Full circumference: \(C=2\pi r\) or \(C=\pi d\).
- Semicircular arc: Half of a circumference, found with \(\pi r\) or \(\frac{\pi d}{2}\).
- Composite figure: A figure formed by combining multiple simple shapes.
- Important idea: Two semicircular arcs with the same diameter have a combined length equal to one full circumference.
📚 What You Should Already Know
Students should know how to find perimeter by adding exposed side lengths, distinguish radius from diameter, use circumference formulas, and recognize that interior measurement lines are not included in a figure’s perimeter.
🚀 What Comes Next
Students will solve more complex perimeter problems involving multiple semicircles, quarter circles, mixed-number dimensions, and composite figures containing several straight and curved edges.
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