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)
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.
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