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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.[1]
Steps
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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 5 centimeter (2.0 in).- 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 10 centimeter (3.9 in), then you can divide it by 2 (10/2) to get 5 centimeter (2.0 in) as the radius.[2]
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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,[3] 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 "5 centimeter (2.0 in)" 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
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Remember to state your answer in units squared. Since you're finding the area of a shape, you'll have to use units square d (such as cm2) in your answer to indicate that you're working with a two-dimensional object.[4] If you're calculating volume, then you'll be working with cubic units (such as cm3).
Video
Community Q&A
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QuestionHow do I find the area of a circle?DonaganTop AnswererMultiply pi by the square of the radius.
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QuestionShould I follow PEMDAS in the formula?DonaganTop AnswererYes, PEMDAS has to be used because of the exponentiation, you have to do that first. If you rewrite it as π×r×r/2 then you don't have to worry about PEMDAS, because it involves only multiplication and division.
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QuestionWhat is the area of a semicircle with the radius of 1.4 m?Community AnswerGiven a radius of circle = 1.4m. As we know, the area of semicircle=((pie)*r*r)/2=(3.14*1.4*1.4)/(2)=3.078 m square.
Tips
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The area of a semicircle is (1/2)(pi)(r^2).Thanks
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The area of a circle is (pi)(r^2)Thanks
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.Thanks
References
- ↑ https://www.mathopenref.com/semicircle.html
- ↑ https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/e/area-and-circumference-of-parts-of-circles
- ↑ https://www.mathsisfun.com/geometry/circle-area-by-sectors.html
- ↑ https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/e/area-and-circumference-of-parts-of-circles
- https://www.mathopenref.com/semicircle.html
About This Article
To find the area of a semicircle, start by finding the area of the full circle using the formula πr^2, where r is the radius of the circle. If you don't know the radius, you can find it by dividing the diameter of the circle by 2. Once you've found the area of the full circle, just divide it by 2 to find the area of the semicircle. If you want to learn how to label your answer with the correct units, keep reading the article!
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