Study Guides/Maths/Circumference of a Semicircle
Study Guide · Maths

Circumference of a Semicircle Formula and Examples

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.

Question (Click to Flip)

What is the formula for the circumference of a semicircle?

Answer

The formula is πr + 2r (or πr + d). You must add the curved boundary (πr) and the straight bottom edge (2r) together.

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Key Facts

Circle Circumference: 2πr.

Semicircle Perimeter: πr + 2r (or πr + d).

Common Mistake: Forgetting to add the straight edge (diameter).

The Formula

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)

Solved Example

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

Questions and Answers

What is the formula for the circumference of a semicircle?+

The formula is πr + 2r (or πr + d). You must add the curved boundary (πr) and the straight bottom edge (2r) together.

If the radius of a semicircle is 7cm, what is its perimeter?+

Using πr + 2r: (22/7 × 7) + (2 × 7) = 22 + 14 = 36 cm.

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