The Semicircle Below Has Diameter 20 Find the Area of the Blue Region

Steps

1. 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 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]

2. 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,^[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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3. 3

   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).

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Add New Question

• Question

  How do I find the area of a circle?

  

  Multiply pi by the square of the radius.

• Question

  Should I follow PEMDAS in the formula?

  

  You don't have to worry about PEMDAS, because the formula involves only multiplication and division.

• Question

  What is the area of a semicircle with the radius of 1.4 m?

  

  Given 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.

• Question

  How do you find the radius of a semicircle when you have the perimeter?

  

  This question uses the concept of circumference rather than area, so be sure to read about calculating the circumference of a circle. To find the radius from the perimeter, you need to know that the perimeter (also called "circumference" when talking about a full circle) of a full circle is given by 2*pi*r. Since we need the perimeter of a semicircle instead of a full circle, divide this by 2 (since the arc length is half) but then add the diameter, which is two times the radius (to account for the straight part across the bottom). So, perimeter of semicircle = (2*pi*r)/2 + 2r = (2 + pi)r. Solve for r = perimeter / (2 + pi), and you have your radius!

• Question

  Why do we need to divide it by 2?

  

  Because "semi" means "half."

• Question

  What is the perimeter if the semicircle's diameter is 12cm?

  

  If you're asking about the circumference of a semicircle (the length of the arc), a full circle's circumference is pi multiplied by the diameter, so a semicircle's circumference would be half that.

• Question

  If the area of a semicircle is 25.12 square meters, what is the diameter?

  

  First multiply the area by 2. Then divide by pi. Then take the square root. Then double that number and you get the diameter in meters.

• Question

  What if there is no number given, and I'm supposed to just find the area of the circle without any clue?

  

  If you don't know the radius, diameter, or circumference, you can't find the area.

• Question

  What is the area of half a semi circle?

  

  The area of a circle is πr², where r is the radius of the circle. The area of half the semicircle is one-quarter of that.

• Question

  How do I find the total perimeter of an object that measures 3cm, 5cm, 7cm, 2cm, 10cm and 7cm?

  

  LyKaxandra Caimoy

  Community Answer

  If the values you gave are the measurements of the sides, you just need to add them.

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Video

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

• The area of a circle is (pi)(r^2)

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• 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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About This Article

Article Summary X

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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Source: https://www.wikihow.com/Find-the-Area-of-a-Semicircle

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