Perimeter of Semicircles
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 13: Circles and Area) learn to calculate the perimeter of semicircles using P = pi*r or P = pi*d/2. This curved-edge-only measurement is essential when calculating the perimeter of composite figures with semicircular parts.
Key Concepts
The perimeter of a semicircle is half the circumference of a complete circle: $$P {semicircle} = \frac{C}{2} = \frac{\pi d}{2}$$ where $d$ is the diameter, or equivalently $$P {semicircle} = \pi r$$ where $r$ is the radius.
Common Questions
What is the formula for the perimeter of a semicircle?
The perimeter of a semicircle (curved edge only) is P = pi times r or equivalently P = pi times d divided by 2. For example, a semicircle with diameter 8 cm has P = 4 pi approximately 12.57 cm.
Does the perimeter formula include the diameter?
The formula P = pi times r gives only the curved arc. When finding perimeter of a composite figure, add any straight edges separately.
How do you find semicircle perimeter from radius vs diameter?
From radius: P = pi times r. From diameter: P = pi times d divided by 2. Both give the same result since r = d/2.
What chapter in Big Ideas Math Advanced 2 covers perimeter of semicircles?
Chapter 13: Circles and Area in Big Ideas Math Advanced 2 (Grade 7) covers perimeter of semicircles.
Why is semicircle perimeter pi times r instead of 2 pi r?
The full circumference is 2 pi r. A semicircle is half a circle, so its curved arc is half the full circumference: (2 pi r) / 2 = pi r.