6 Tricks for finding the Area of a Semicircle

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Here’s how to find the Area of a Semicircle

The Area of a Semicircle is all of the area that is inside of a semicircle. The way you find the Area of a Semicircle is similar to how you find the area of a circle. Usually you find the area of a semicircle using radius but sometimes you will have to find the Area of a Semicircle with diameter. The diameter is twice as long as the radius, or the radius is half of the diameter. The formula for how to find Area of a Semicircle is area equals pi times the radius squared then divided by two. If you have the area of a semicircle with diameter that means that you have to divide the diameter by two to get the radius. Once you have the radius you can use the Area of a Circle formula. When simplifying you need to do follow the order of operations. You must square the radius and then multiply it times pi and then finally divide by two.

Common Core Standard: 7.G.5

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The easy way to answer Area of a Semicircle Example Problems

Read the guide below to learn how to find area of a semi circle.

The Area of a Semicircle is the area that is within a semicircle. Typically you discover the area of a semicircle by utilizing the radius of the semicircle, however you can discover the semi circle area with diameter. The diameter is twice the length of the radius, in other words, the radius is half of the diameter. The equation for how to discover Area of a Semicircle is pi times the radius squared divided by two equals the area. In the event that you have to find the Area of a Semicircle with diameter you have to divide the diameter by two. Then you can utilize the Area of a Semicircle equation.

6 Quick Steps for using the Area of a Semicircle Formula

Use the Area of a Semicircle Formula: Area equals pi time the radius squared then divided by two.
The first step is to square the radius.
Then you multiply the square of the radius times pi. (3.14)
Finally you divide that answer by two.
After you do that make sure you check your units and ensure that they are correct.
If the circle gives you the diameter then you should divide it by two first.

Area of a Semicircle Practice Problems Quiz

Watch the video explanation of our Area of a Semicircle Worksheet

Watch our free video on how to solve Area of a Semicircle. This video shows how to solve problems that are on our free Area of Semicircle worksheet that you can get by submitting your email above.

Watch the free Area of a Semicircle video on YouTube here: Area of a Semicircle Video

Video Transcript:

This video is about how to find the area of a half circle. You can get the area of semi circle worksheet used in this video for free by clicking on the link in the description below.

In order to understand how we find area of a semicircle you first have to understand what a semicircle is. Now a semi-circle is just a fancy math way of saying half circle. This means that when you find the area of a semicircle you’re really just finding the area of half of a circle. So in this case I’m going to shade half of it blue and if you were to find the area of a semicircle that is this sides you would just be finding the area of the blue shaded region. If you know the formula for a circle is area equals pi times the radius squared or pi r squared, then you know the semi circle area formula because a semi-circle is just half of a circle, so all you have to do is take our area of a circle formula and then divide it by 2. This will give us the area of semicircle formula. This blue divided by 2 is just a representation of the semi-circle because it is half of a full circle. Now we know that area of a semi-circle formula is pi times the radius squared then we’re going to divide by 2. Let’s say we were given this as an example and let’s say they said that the radius for this was 10. In order to solve for area of a semicircle you have to take the radius, which in this case is 10 substitute it in for r and then solve based on your formula. Our formula says pi times the radius which in this case is 10. We’re going to substitute 10 in for r squared and then we’re going to divide by 2. According to order of operations the first thing you need to do is square or do the exponent so we’re going to do 10 times 10 which is 100 times pi which is 314.16 divided by 2. And then 314.16 divided by 2 gives us 150 centimeters squared.

Let’s jump to number one on our area of a semi circle worksheet. In order to solve problems involving area of half circle we have to remember our area of a half circle formula that is area equals pi times the radius squared and then divided by 2. In this case we are given the distance from the middle of the circle to the outer edge which is known as the radius. We know that the radius is equal to 6 inches because it’s given to us in order to solve using the formula. We’re going to take our radius which is 6 inches and substitute it in for r into the formula. We take area equals pi times the radius which in this case is 6 squared and then divided by 2. First thing we do according to order of operations is 6 squared so 6 times 6 which is 36 and then we’re going to divide by 2. So then you do pi times 36 which is equal to 113.1 and you can’t forget the divided by 2 and then finally when you divide by 2 you will get 56.55 inches squared as the final solution. This is the first example of how to find area of semicircle.

The next problem on our area of a semi-circle worksheet we’re going to talk about how to find the area of a semi-circle with diameter. We know that the area of a semi-circle is pi times the radius squared and then divided by 2. In the case of this problem they don’t give us the radius they give us the whole diameter which runs all the way across from one side of the circle all the way across to the other. We know this is equal to the diameter or 3 feet is equal to the diameter so in order to get the radius from the diameter you have to divide by two because diameter is twice the size of the radius. To get the radius all you do is you take the diameter divide by 2. So 3 divided by 2 is 1.5 feet so now we know the radius is 1.5 and then you follow the same procedure that you did in the previous problem. You take the radius which is 1.5 and you substitute it in where r used to be. Area is equal to pi times the radius which is 1.5 squared and then you’re going to divide it by 2. You do 1.5 times 1.5 which is 2.25 then you’re going to do pi times 2.25 and that will give you 7.07 divided by 2 and your final answer will be 3.53 feet squared. The only extra step in finding the area of a circle with the diameter is having to divide the diameter by 2 to get the radius.