Find the Area of a Semicircle

A semi-circle is half of a circle. Therefore, to find the area of a semi-circle, you just have to find the area of a full circle and then divide it by two. It will be faster than you think.

Steps

  1. Find the radius of the semi-circle. You'll need the radius to find the area of the semi-circle. Let's say the radius of the semi-circle is {{safesubst:#invoke:convert|convert}}.
    • If you're only given the diameter of the circle, you can divide it by two to get the radius. For example, if the diameter of the circle is {{safesubst:#invoke:convert|convert}}, then you can divide it by 2 (10/2) to get {{safesubst:#invoke:convert|convert}} as the radius.
  2. Find the area of the full circle and divide it by two. The formula for finding the area of a full circle is πr2, where "r" represents the radius of the circle. Since you're finding the area of a semi-circle, you'll be looking for half of the area of a circle, which means you have to use the formula for finding the area of a semi-circle and then divide it by two. So, the formula you'll have to use to find the area of a semi-circle is πr2/2. Now, just plug "{{safesubst:#invoke:convert|convert}}" into the formula to get your answer. You can either use the closest approximation for π with your calculator, substitute 3.14 for π, or you can just leave the symbol in place. Here's how you do it:
    • Area = (πr2)/2
    • Area = (π x 5 cm x 5 cm)/2
    • Area = (π x 25 cm2)/2
    • Area = (3.14 x 25 cm2)/2
    • Area = 39.25 cm2
  3. Remember to state your answer in square units. Since you're finding the area of a shape, you'll have to use square units (such as cm2) in your answer to indicate that you're working with a two-dimensional object. If you're calculating volume, then you'll be working with cubic units (such as cm3).



Tips

  • The area of a semicircle is (1/2)(pi)(r^2).
  • The area of a circle is (pi)(r^2)

Warnings

  • Be careful not to use the diameter in the formula for finding area! If the diameter is given, then remember to divide it by 2 to get the radius.

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Sources and Citations

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