how to find the area of a half circle
A semicircle is formed when a lining passing through the centre touches the two ends on the circle.
In the below figure, the line AC is called the diameter of the circle. The diameter divides the circle into two halves such that they are equal in area. These two halves are referred to as the semicircles. The area of a semicircle is half of the area of a circle.
A circle is a locus of points equidistant from a given point which is the centre of the circle. The common distance from the centre of a circle to its point is called a radius.
Thus, the circle is entirely defined by its centre (O) and radius (r).
Area of Semi Circle
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.
Area of Semicircle = 1/2 (π r2)
Perimeter of Semicircle
The perimeter of a semicircle is the sum of the half of the circumference of the circle and diameter. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d orπr + 2r, where r is the radius.
Therefore,
Or
Circumference = (πr + 2r)
Semi Circle Shape
When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get semicircular shape.
Since semicircle is half that of a circle, hence the area will be half that of a circle.
The area of a circle is the number of square units inside that circle.
Let us generate the above figure. This polygon can be broken into n isosceles triangle (equal sides being radius).
Thus, one such isosceles triangle can be represented as shown below.
The area of this triangle is given as ½(h*s)
Now for n number of polygons, the area of a polygon is given as
½(n*h*s)
The term n × s is equal to the perimeter of the polygon. As the polygon gets to look more and more like a circle, the value approaches the circle circumference, which is 2 × π × r. So, substituting 2×π×r for n × s.
Polygon area = h/2(2 × π × r)
Also, as the number of sides increases, the triangle gets narrower and so when s approaches zero, h and r have the same length. So substituting r for h:
Polygon area = h/2(2 × π × r)
= (2 × r × r × π)/2
Rearranging this we get
Area = πr2
Now the area of a semicircle is equal to half of that of a full circle.
Therefore,
Area of a semicircle =(πr2)/2
Semi circle Formula
The below table shows the formulas associated with the semicircle of radius r.
| Area | (πr2)/2 |
| Perimeter (Circumference) | (½)πd + d; when diameter (d) is known |
| πr + 2r | |
| Angle in a semicircle | 90 degrees, i.e. right angle |
| Central angle | 180 degrees |
Semi circle Examples
Example 1:
Find the area of a semicircle of radius 28 cm.
Solution:
Given,
Radius of semi circle = r = 28 cm
Area of semi circle = (πr2)/2
= (½) × (22/7) × 28 × 28
= 1232
Therefore, the area of the semi circle is 1232 sq.cm.
Example 2:
What is the perimeter of a semicircle with diameter 7 cm?
Solution:
Given,
Diameter of semicircle = d = 7 cm
Formula for the circumference (perimeter) of a semicircle using its diameter = (½)πd + d
Substitute the value of d, we get;
= (½) × (22/7) × 7 + 7
= 11 + 7
= 18
Therefore, the perimeter of the semicircle is 18 cm.
Frequently Asked Questions on Semicircle
Is a semicircle half the circle?
Yes, a semicircle is half the circle. That means, a circle can be divided into two semicircles.
What shape is a semicircle?
The shape of a semicircle will be obtained by cutting a circle along its diameter and the full arc of a semicircle always measures 180 degrees. Example of a semicircular shape is protractor.
What is the semicircle angle?
The angle made by the triangle in a semicircle is right angle, i.e. 90 degrees.
What is the area of a semicircle?
The area of a semicircle with radius r is equal to half the area of the circle.
Area of semicircle = (1/2) × Area of circle = (1/2)πr^2
What is the perimeter formula of a semicircle?
The perimeter formula of semicircle of radius r is given by:
Semicircle circumference = (1/2)2πr + 2π = πr + 2r
how to find the area of a half circle
Source: https://byjus.com/maths/semi-circle/
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