A semicircle is exactly half of a full circle. While finding the area is simple (just divide the area of a circle by 2), finding the circumference (or perimeter) of a semicircle requires a bit more thought.
Circle Circumference: 2πr.
Semicircle Perimeter: πr + 2r (or πr + d).
Common Mistake: Forgetting to add the straight edge (diameter).
Many students make the mistake of thinking the circumference of a semicircle is just half the circumference of a circle (πr). This is wrong for a solid shape!
When you cut a circle in half, you expose the straight flat edge at the bottom — which is the diameter (d).
Therefore, the total boundary (perimeter/circumference) is: Perimeter of Semicircle = Curved arc + Straight base P = (½ × 2πr) + d P = πr + d Since diameter d = 2r, the most common formula is: Perimeter = πr + 2r or r(π + 2)
Question: Find the perimeter of a semicircular park with a radius of 7m. (Use π = 22/7)
Solution: Radius (r) = 7m Formula: P = πr + 2r Curved part (πr) = (22/7) × 7 = 22m Straight part (2r) = 2 × 7 = 14m Total Perimeter = 22 + 14 = 36m
The formula is πr + 2r (or πr + d). You must add the curved boundary (πr) and the straight bottom edge (2r) together.
Using πr + 2r: (22/7 × 7) + (2 × 7) = 22 + 14 = 36 cm.
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