How To Calculate The Area of a Semicircle

in this video we're going to talk about how to calculate the area of semi-circle now in this problem we're given the radius of the semicircle and that's 4 feet so let's begin by drawing picture semi means half so what we have is half of circle the radius is the distance between the center of the circle and any point on the edge of the circle so this is 4 feet that's the radius now we need to know the formula to calculate the area of circle the area of circle is pi squared that that's full circle now to calculate the area of semicircle we need to basically take half of this value so the area of semicircle is just one half pi squared now once you have the radius all you need to do is plug in the radius into this formula and that is going to give you the answer so let's go ahead and do that so it's going to be one half pi times four feet squared so for pi i'm going to use the value 3.14159 4 squared is 16. so it's going to be 16 times 3.14159 times 0.5 so the area of the semicircle in this example is 25.13 now what are the units for area in this problem area is always in square units the radius is in feet so the area in this example is going to be square feet so it's 25.13 square feet so that's how you can calculate the area of semicircle if you're given the radius of the semicircle now let's work on similar but different problem calculate the area of semi-circle with diameter of 14 centimeters so feel free to pause the video if you want to try this problem so like before we're going to begin by drawing picture the diameter is the distance between two points on the edge of the circle but it must pass through the center of the circle now what you need to know is that the diameter is twice the value of the radius so the radius is basically one half of the diameter so if the diameter is 14 centimeters that means that the radius of the circle is half of 14. half of 14 is seven so the radius is seven centimeters now that we know the radius of the semicircle this problem becomes very similar to the previous problem all we need to do is use the formula to calculate the area of the semicircle plug in the radius and that's going to give us the answer so for pi i'm going to use the same value of 3.14159 and in this example the radius is going to be seven centimeters so first we have seven squared or seven times seven that's 49 and then we're going to multiply that by 3.14 and then times 0.5 so the answer that got for this problem is 76.97 square centimeters so that's the area of this particular semi-circle so that's basically it for this video now you know how to calculate the area of semi-circle given not only its radius but also the diameter as well now i'm going to be posting another video to youtube and that is how to find the perimeter of semicircle so for those of you who want to see it when it's uploaded just go to the youtube search bar type in perimeter of semicircle and then type in organic chemistry tutor it should come up and also i'll be posting few links in the description section below of this video to some other video content that have that relates to this topic so feel free to take look at that if you're interested and don't forget to hit that subscribe button if you like this video thanks for watching