How to Find the Perimeter of a Semi Circle

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The continuous closed line that makes the boundary of a two-dimensional shape is known as the perimeter. It’s easy to work out the perimeter of a shape with straight edges, such as a square, because you simply add the lengths of each edge together. A different formula is required to work out the perimeter of a semi circle (a circle cut in half), because it consists of a curved edge as well as a straight edge. That formula is

P = \frac{1}{2} πd + d

where ​d​ is the diameter of the semi circle.

  1. Remember Pi Constant

  2. Apply the number pi (π) to the formula

    P = \frac{1}{2} πd + d

    Pi is a circle's circumference divided by its diameter and is always the same value, 3.14.

  3. Note the Diameter

  4. To find the perimeter of a semi circle, you have to know the diameter (the length of its straight edge). For example, if the diameter of your semi circle is 12 centimeters, the formula becomes

    P = \frac{1}{2} ×(3.14×12) + 12
  5. Break Down the Equation

  6. Work out

    3.14 × 12 = 37.68

    Then work out

    37.68 ÷ 2 = 18.84

    You now have the perimeter of the curved edge of the semi circle. But a semi circle also has a straight edge, which is why you have to add the length of the diameter to calculate the whole perimeter. In this case, work out

    18.84 + 12 = 30.84

    The perimeter of your semi circle is 30.84 centimeters.


About the Author

Claire is a writer and editor with 18 years' experience. She writes about science and health for a range of digital publications, including Reader's Digest, HealthCentral, Vice and Zocdoc.