A semicircle is created when a lining passing through the centre touches the 2 ends on the circle.
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In the below figure, the line AC is dubbed the diameter the the circle. The diameter divides the circle right into two halves such the they space equal in area. These 2 halves are described as the semicircles. The area of a semicircle is half of the area of a circle.
A one is a locus of clues equidistant native a given point which is the centre of the circle. The common distance indigenous the centre of a circle come its suggest is referred to as a radius.
Thus, the one is entirely identified by its center (O) and also radius (r).
Area of Semi Circle
The area of a semicircle is half of the area of the circle. As the area of a one is πr2. So, the area the a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.
Area that Semicircle = 1/2 (π r2) |
Perimeter of Semicircle
The perimeter the a semicircle is the amount of the half of the circumference of the circle and diameter. Together the perimeter of a circle is 2πr or πd. So, the perimeter that a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius.
Therefore,
The perimeter that Semicircle = (1/2) π d + d Or Circumference = (πr + 2r) |
Semi circle Shape
When a one is cut into 2 halves or when the circumference of a one is split by 2, we acquire semicircular shape.
Since semicircle is fifty percent that the a circle, thus the area will certainly be fifty percent that the a circle.
The area of a one is the number of square systems inside that circle.
Let us generate the above figure. This polygon deserve to be damaged into n isosceles triangle (equal sides being radius).
Thus, one such isosceles triangle have the right to be stood for as presented below.
The area of this triangle is provided as ½(h*s)
Now for n number of polygons, the area the a polygon is offered as
½(n*h*s)
The hatchet n × s is same to the perimeter the the polygon. As the polygon gets to look much more and more like a circle, the value approaches the one circumference, i m sorry is 2 × π × r. So, substituting 2×π×r because that n × s.
Polygon area = h/2(2 × π × r)
Also, as the number of sides increases, the triangle gets narrower and so as soon as s philosophies zero, h and r have actually the very same length. Therefore 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 the a semicircle is equal to fifty percent of the of a complete circle.
Therefore,
Area of a semicircle =(πr2)/2
Semi circle Formula
The below table shows the formulas associated with the semicircle the radius r.
Area | (πr2)/2 |
Perimeter (Circumference) | (½)πd + d; as soon as diameter (d) is known |
πr + 2r | |
Angle in a semicircle | 90 degrees, i.e. Right angle |
Central angle | 180 degrees |
Semi one Examples
Example 1:
Find the area that a semicircle of radius 28 cm.
Solution:
Given,
Radius that semi one = r = 28 cm
Area the semi one = (πr2)/2
= (½) × (22/7) × 28 × 28
= 1232
Therefore, the area the the semi one is 1232 sq.cm.
Example 2:
What is the perimeter the a semicircle with diameter 7 cm?
Solution:
Given,
Diameter the semicircle = d = 7 cm
Formula because that the one (perimeter) the a semicircle making use of its diameter = (½)πd + d
Substitute the value of d, we get;
= (½) × (22/7) × 7 + 7
= 11 + 7
= 18
Therefore, the perimeter that the semicircle is 18 cm.
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Frequently Asked inquiries on Semicircle
Is a semicircle fifty percent the circle?
Yes, a semicircle is half the circle. The means, a circle can be separated into two semicircles.