Education

How to Find the Area and Perimeter of a Semi-Circle

Written by Jimmy Rustling

A semicircle is said to be formed when a line passing through the center touches the two ends of the circle. A circle is a collection of points that are all equidistant from the circle’s center. A radius is a common distance between a circle’s center and its point.

As a result, the circle is completely defined by its center (O) and radius (R) (r). In this blog, we are going to explore the semi-circle and learn how to find the area and perimeter of semicircle.

Definition of a Semicircle

A semicircle is formed when a circle is sliced in half along its diameter. The two sections of the cut area of equal proportions. A semicircle, also known as a half-disk, is a round paper plate that has been folded in half. In the semicircle, there is one line of symmetry that is known as reflection symmetry. The semicircle is half of a 360-degree circle, hence the a.

Area of a SemiCircle

The region or interior space of a circle is referred to as the circle’s area. Because a semicircle is half a circle, the area of a semicircle will be half that of a circle. A semicircle has half the surface area of a circle. Because the radius of a circle is r², As a result, the radius of a semicircle is 1/2(πr²), and the area of a semicircle is πr². 3.14 or 22/7 is the value.

Area of Semicircle = 1/2 (πr²)

Perimeter of a Semicircle

The perimeter of a semicircle is not the same as its area, i.e. the perimeter is not half the circumference of a circle. We need to know the diameter or radius of a circle, as well as the length of the arc, to compute the perimeter of a semicircle. The perimeter of a semicircle is equal to half of the circle’s circumference plus the diameter. The circumference of a circle is expressed as, 2πr or πd. A semicircle’s perimeter is 1/2 (πd) + d or πr + 2r, where r is the radius.

As a result, the perimeter of Semicircle is equal to (1/2) π d + d or (πr + 2r)

Shape: Semi-circle

We get a semicircular shape when a circle is sliced in half or when the circumference of a circle is divided by two. The protractor, or semicircle, is one of the most popular shapes in geometry. A semicircle is half of a circle, and real-life examples include a railway tunnel through which a train goes, an igloo, half of a watermelon, and many others. On a 2D plane, all of these forms resemble a semi-circle. We’ll learn more about semicircles in this post.

Because the area of a semicircle is half that of a circle, the area of a semicircle will be half that of a circle. The number of square units inside a circle is the circle’s area.

How do you Get the Formula for a Semicircle’s Area?

Let’s look at how the area of a semicircle formula is calculated.

Here’s a quick interactive simulation to help you understand the formula’s notion.

  • Imagine how the circle transforms into a triangle in the simulation above, and how the radius becomes the triangle’s height, while the circumference, which is 2r, becomes its base.
  • We know that the area of a triangle can be calculated by multiplying the base by the height and then dividing by two.
  • After simplifying this, we get the area of the circle as πr2 Area of Circle=πr2
  • Now the area of the semicircle is half the area of the circle.
  • Therefore, the area of the semicircle is stated as above.

Semicircular Circumference

Because the perimeter is half the circumference of the circle, the circumference of a semicircle is considered the same as the semicircle perimeter. A semicircle also has a straight line that is the circle’s diameter and describes the distance around the shape. As a result

Circumference of a Semicircle = πR + 2R units

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About the author

Jimmy Rustling

Born at an early age, Jimmy Rustling has found solace and comfort knowing that his humble actions have made this multiverse a better place for every man, woman and child ever known to exist. Dr. Jimmy Rustling has won many awards for excellence in writing including fourteen Peabody awards and a handful of Pulitzer Prizes. When Jimmies are not being Rustled the kind Dr. enjoys being an amazing husband to his beautiful, soulmate; Anastasia, a Russian mail order bride of almost 2 months. Dr. Rustling also spends 12-15 hours each day teaching their adopted 8-year-old Syrian refugee daughter how to read and write.