What is a Semicircle?
A semicircle can be defined as a one-dimensional locus of points that forms half of a circle. In other words, we can say that a semicircle is the half circle that gets formed by cutting a whole circle into two halves along the diameter. While studying this topic, there are various concepts that a child must learn, such as perimeter and area of semicircle. In this article, we will explore further details of a few properties and concepts associated with a semicircle.
Properties of a Semicircle
- The full arc of a semicircle measures 180 degrees as a semicircle is half of a circle (360 degrees).
- A semicircle has only one line of symmetry. This is the reflection symmetry.
- The longest chord of a circle, also known as the diameter, cuts the circle into two equal semicircles.
- A semicircle is also known as a half-disk in layman’s terms because it is a two-dimensional geometric shape that also includes the diameter segments from one end of the arc to the other end. It also encompasses all the interior points.
- If a triangle is inscribed in a semicircle with two vertices at the endpoints and one vertex elsewhere on the semicircle, then the triangle formed is a right-angled triangle.
- If a line is intersecting the semicircle perpendicularly, then it is concurrent at the center of the circle forming the given semicircle.
Area of a Semicircle
The area of a semicircle is defined as the 2D space enclosed within the boundary of the semicircle. As a semicircle is half of a circle hence, the area of a semicircle is also half of the area of a circle. It is measured in square units.
Area of a semicircle = Area of a circle/2 = πr2 / 2
where is the constant pi and is given by either 3.14 or 22/7 and r is the radius of the semicircle.
Perimeter of a Semicircle
The perimeter of a semicircle is defined as the total length of the boundary of the semicircle. Thus, we can say that the sum of the diameter and the half of the circumference of the circle will form the perimeter of a semicircle.
Perimeter of a semicircle = half of the circumference of a circle + diameter = ½ (2πr) + 2r = πr + 2r = r (π + 2)
Example: If the diameter of a semicircle is given by 14cm find the area and perimeter.
Solution: As the radius is half of the diameter hence, r = 7cm.
Area of a semicircle = πr2 / 2 = π72 / 2 = 77 cm2
Perimeter of a semicircle = r (π + 2) = 7(π + 2) = 36 cm
There are many topics associated with semicircles in geometry. Thus, kids must have a good understanding of the basics as all similar topics are interrelated. One of the best ways to build a solid knowledge base is by joining an online tutoring platform such as Cuemath.
At Cuemath, the certified math experts use various resources such as interactive worksheets, workbooks, online math games, puzzles, apps, and visual simulations to teach a lecture. They believe in giving cues to a child if they encounter difficulties while solving problems. Kids are encouraged to improve their reasoning, logical and cognitive abilities.
The teachers work to ensure that children can combine fun with studies to have an enjoyable learning experience. So you should consider hiring a maths tutor for your child. With the proper guidance, children can instill crystal clear concepts and can solve challenging problems within no time. Hopefully, this article gives you an insight into how to approach the topic of semicircles, and I wish you all the best!