How to Find Area of a Semicircle: Formula, Examples, Worksheets

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How to find Area of a Semicircle | 7th Grade | Mathcation

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Key Points about Area of a Semicircle

The area of a semicircle is half the area of a circle with the same radius.
The formula for the area of a semicircle is πr²/2 or π(d/2)²/2.
The area of a semicircle can be used in real-world applications such as calculating the area of a half-circle shaped swimming pool or the area of a curved section of a garden bed.

How to find the Area of a Semicircle

The area of a semicircle is the amount of space inside half of a circle. It is a fundamental concept in geometry and is used in many real-world applications. The formula for the area of a semicircle is derived from the formula for the area of a circle, and it is relatively simple to calculate.

The formula for the area of a semicircle is πr²/2, where r is the radius of the circle. Since a semicircle is half of a circle, you can think of it as a circle with a diameter that is half as long as the diameter of the original circle. Therefore, another way to calculate the area of a semicircle is to use the formula A = π(d/2)²/2, where d is the diameter of the circle.

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
Related Topics: Area of a Circle, Circumference of a Circle, Perimieter of a Semicircle, Complementary Angles, Supplementary Angles, Vertical Angles
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How to find Area of a Semicircle

Understanding the Area of a Semicircle Formula

The area of a semicircle is half the area of a circle with the same radius. The formula for the area of a semicircle is:

A = πr²/2

where A is the area and r is the radius of the semicircle. This formula can be derived by taking half of the formula for the area of a circle, which is πr².

Using a Calculator

Calculating the area of a semicircle can be done manually using the formula above. However, it can also be done quickly and easily using a calculator. Many calculators have a built-in function for calculating the area of a semicircle.

To use a calculator to find the area of a semicircle, follow these steps:

Enter the radius of the semicircle into the calculator.
Press the x² button to square the radius.
Multiply the result by π.
Divide the result by 2.

For example, to find the area of a semicircle with a radius of 5, follow these steps:

Enter 5 into the calculator.
Press the x² button to get 25.
Multiply 25 by π to get 78.54.
Divide 78.54 by 2 to get 39.27.

Therefore, the area of the semicircle is 39.27.

Simple Area of a Semicircle Examples

Example 1

Find the area of a semicircle with a radius of 8.

A = πr²/2
A = π(8)²/2
A = 64π/2
A = 32π
A ≈ 100.53

Therefore, the area of the semicircle is 100.53.

Example 2

Find the area of a semicircle with a radius of 12.5.

A = πr²/2
A = π(12.5)²/2
A = 156.25π/2
A = 78.125π
A ≈ 245.06

Therefore, the area of the semicircle is 245.06.

Example 3

Find the area of a semicircle with a radius of 3.75.

A = πr²/2
A = π(3.75)²/2
A = 14.0625π/2
A = 7.03125π
A ≈ 22.12

Therefore, the area of the semicircle is 22.12.

Finding Area of a Semicircle with Diameter

A semicircle is a half of a circle. The formula for the area of a semicircle is half of the formula for the area of a circle. The area of a circle is πr², where r is the radius of the circle. Therefore, the area of a semicircle is half of πr² or (πr²)/2.

To find the area of a semicircle with diameter, you first need to find the radius of the semicircle. The radius is half of the diameter. So, if the diameter of the semicircle is d, then the radius is d/2.

Once you have the radius, you can use the formula for the area of a semicircle. The formula is (πr²)/2, where r is the radius of the semicircle. So, the area of a semicircle with diameter d is (π(d/2)²)/2 or (πd²)/8.

Here is an example: if the diameter of a semicircle is 8 cm, then the radius is 4 cm. The area of the semicircle is (π(4)²)/2 or 8π cm².

Examples of Finding Area of a Semicircle

To calculate the area of a semicircle, the formula is A = (πr^2)/2, where r is the radius of the semicircle. Here are some examples of finding the area of a semicircle.

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.

Example 1:

Suppose the radius of a semicircle is 5 cm. The area of the semicircle can be calculated as follows:

A = (πr^2)/2 = (π x 5^2)/2 = 39.27 cm^2

Therefore, the area of the semicircle is 39.27 cm^2.

Example 2:

Suppose the diameter of a semicircle is 12 cm. To find the radius, divide the diameter by 2. Therefore, the radius is 6 cm. The area of the semicircle can be calculated as follows:

A = (πr^2)/2 = (π x 6^2)/2 = 56.55 cm^2

Therefore, the area of the semicircle is 56.55 cm^2.

Example 3:

Suppose the radius of a semicircle is 8.5 m. The area of the semicircle can be calculated as follows:

A = (πr^2)/2 = (π x 8.5^2)/2 = 113.04 m^2

Therefore, the area of the semicircle is 113.04 m^2.

Example 4:

Suppose the diameter of a semicircle is 16 inches. To find the radius, divide the diameter by 2. Therefore, the radius is 8 inches. The area of the semicircle can be calculated as follows:

A = (πr^2)/2 = (π x 8^2)/2 = 100.53 in^2

Therefore, the area of the semicircle is 100.53 in^2.

These examples demonstrate how to find the area of a semicircle using the formula A = (πr^2)/2. By knowing the radius or diameter of the semicircle, one can easily calculate its area.

5 Quick Area of a Semicircle Practice Problems

What is the Area of a Semicircle?

A semicircle is a two-dimensional shape that is formed by dividing a circle into two equal parts. It is a half circle, and it has a curved edge and a straight edge. The area of a semicircle is the amount of space enclosed within the boundary of a semicircle. It is expressed in square units like cm², m², yd², ft², etc.

To calculate the area of a semicircle, you need to know the radius of the circle. The radius is the distance from the center of the circle to its edge. The formula for the area of a semicircle is half of the area of a circle.

Area of a Semicircle = 1/2 x π x r²

Where r is the radius of the circle, and π is the mathematical constant pi, which is approximately equal to 3.14159.

For example, if the radius of a semicircle is 5 cm, then the area of the semicircle would be:

Area of a Semicircle = 1/2 x π x r²
Area of a Semicircle = 1/2 x π x 5²
Area of a Semicircle = 1/2 x π x 25
Area of a Semicircle = 1/2 x 3.14159 x 25
Area of a Semicircle = 39.27 cm²

In summary, the area of a semicircle is half of the area of a circle. To calculate the area of a semicircle, you need to know the radius of the circle, and you can use the formula 1/2 x π x r².

Area of a Semicircle and Rectangle

A semicircle is half of a circle, and its area is just half of the area of a full circle. The formula to calculate the area of a semicircle is A = (πr²)/2, where A represents the area and r represents the radius of the semicircle.

If a semicircle is combined with a rectangle, the area of the resulting shape can be calculated by finding the area of each shape and adding them together. The formula for the area of a rectangle is A = lw, where A represents the area, l represents the length, and w represents the width of the rectangle.

To find the area of a shape that combines a rectangle and a semicircle, follow these steps:

Calculate the area of the rectangle by multiplying its length and width.
Calculate the area of the semicircle by using the formula A = (πr²)/2, where r is the radius of the semicircle.
Add the area of the rectangle and the area of the semicircle together to find the total area of the shape.

For example, consider a shape that has a rectangle with a length of 8 cm and a width of 4 cm, and a semicircle with a radius of 3 cm attached to one of its ends.

The area of the rectangle is A = lw = 8 cm x 4 cm = 32 cm².

The area of the semicircle is A = (πr²)/2 = (π x 3²)/2 = 4.5π cm².

The total area of the shape is the sum of the area of the rectangle and the area of the semicircle, which is 32 cm² + 4.5π cm².

It is important to note that when working with a semicircle and rectangle combination, the diameter of the semicircle must be equal to the width of the rectangle. If the diameter of the semicircle is not equal to the width of the rectangle, the shape cannot be divided into a rectangle and a semicircle, and the formula for finding the area of the shape will be different.

FAQ about Finding Area of a Semicircle

What is the formula of area of semicircle?

The formula for the area of a semicircle is half the area of a circle. The formula for the area of a circle is πr², where r is the radius of the circle. Therefore, the formula for the area of a semicircle is ½ × πr².

What is the radius of semicircle formula?

The radius of a semicircle is half the diameter of the circle. The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. Therefore, the formula for the radius of a semicircle is r = d/4.

What is the circumference of a semicircle area?

The circumference of a semicircle is half the circumference of a circle. The formula for the circumference of a circle is 2πr, where r is the radius of the circle. Therefore, the formula for the circumference of a semicircle is πr.

What is the area of a semicircle with a radius of 6?

The area of a semicircle with a radius of 6 can be found by using the formula for the area of a semicircle, which is ½ × πr². Substituting the value of r as 6, we get the area of a semicircle as ½ × π × 6² = 18π.

How to Find the Area of Semicircle Using Diameter?

To find the area of a semicircle using diameter, first, find the radius of the semicircle by dividing the diameter by 2. Once the radius is known, use the formula for the area of a semicircle, which is ½ × πr², where r is the radius of the semicircle.

Is a semicircle half the circle?

Yes, a semicircle is half the circle. A semicircle is formed by cutting a circle into two equal halves, and each half is called a semicircle.

Area of a Semicircle Worksheet Video Explanation

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.