How To Calculate The Perimeter of a Semicircle

in this video we're going to talk about how to calculate the perimeter of semi-circle given the radius of that object so let's begin with picture semi-circle is basically half of circle and the radius is the distance between the center of the circle and any point on the circle so this would be the radius of the circle and we know that the radius of the circle is eight inches now what we need to do is calculate the perimeter of the semicircle that's basically the distance that wraps around the entire figure so how can we calculate the perimeter of semicircle well we need to break it up into parts first we need to be familiar with the circumference of circle the circumference of circle is equal to 2 pi and it is the distance or the perimeter around that circle so if the circumference of an entire circle is 2 pi what is the circumference of semi-circle or half circle well in that case the circumference will be just half of 2 pi or simply pi and then this part here is just the diameter which is twice the radius so the perimeter of semicircle is equal to the diameter which is this part plus half of the circumference of circle which is pi times and the diameter is two times the radius so it's going to be two plus pi times and if you want to you can factor out the radius so you can say that the perimeter is going to be the radius times pi plus 2. so let's use that formula to get the answer the radius in this example is 8 inches pi if you want to convert that to decimal is approximately 3.14159 and then plus 2. so add in these two numbers that's going to be 5.14159 multiplying that by eight we get perimeter that is approximately 41.1 inches so that's how we can calculate the perimeter of semicircle now what about this problem what is the perimeter of semicircle with an area of hundred point five three one square centimeters so feel free to pause the video and work on that example so let's rewrite the formula for calculating the perimeter so we said that it's equal to the radius of the semicircle times pi plus 2. now we're given the area of the semicircle so we could use that to calculate the radius the area of semi-circle is one-half pi squared so we have an area of 100.531 pi is 3.14159 and then we can calculate so first let's multiply 3.14159 by 0.5 so that's 1.570795 and then let's isolate squared by dividing both sides by this number so on the right these two numbers will cancel giving us squared on the left it's going to be hundred point five three one divided by one point five seven zero seven nine five and that is sixty four now we can take the square root of both sides the square root of 64 is eight so the radius is about eight centimeters now we can take this answer and plug it into this formula so the radius is eight centimeters and then we can multiply by pi plus two so if you want an exact answer it would be eight pi plus sixteen you distribute eight to pi and to two as well so this would be the exact answer for the perimeter of the circle but let's get decimal answer so instead of using pi i'm going to use 3.14159 and it turns out that this problem is going to be the same as the last one 5.14159 times 8 gives us the same answer of 41.1 centimeters what are the chances of that so that's it for this video now you know how to calculate the perimeter of semicircle