A semicircle is formed when a lining passing with the centre touches the 2 ends top top the circle.
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In the listed 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 2 halves are referred to as the semicircles. The area that a semicircle is fifty percent of the area the a circle.
A one is a locus of clues equidistant native a given allude which is the center of the circle. The common distance indigenous the center of a circle to its suggest is dubbed a radius.
Thus, the circle is entirely identified by its centre (O) and radius (r).
Area of Semi Circle
The area that a semicircle is fifty percent of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), wherein r is the radius. The value of π is 3.14 or 22/7.
Area of Semicircle = 1/2 (π r2) |
Perimeter that Semicircle
The perimeter that a semicircle is the amount of the fifty percent of the circumference of the circle and also diameter. As the perimeter the a one 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 of Semicircle = (1/2) π d + d Or Circumference = (πr + 2r) |
Semi one Shape
When a one is reduced into 2 halves or once the one of a one is separated by 2, we obtain semicircular shape.
Since semicircle is half that that a circle, for this reason the area will be fifty percent that of a circle.
The area of a circle is the number of square devices inside the circle.
Let united state generate the above figure. This polygon deserve to be broken into n isosceles triangle (equal sides gift radius).
Thus, one such isosceles triangle deserve to be represented as shown below.
The area that this triangle is offered as ½(h*s)
Now because that n variety of polygons, the area of a polygon is given as
½(n*h*s)
The hatchet n × s is equal to the perimeter the the polygon. As the polygon gets to look an ext and an ext like a circle, the value philosophies the circle circumference, which is 2 × π × r. So, substituting 2×π×r because that n × s.
Polygon area = h/2(2 × π × r)
Also, together the number of sides increases, the triangle it s okay narrower and so when s approaches zero, h and r have the same length. For this reason substituting r because that h:
Polygon area = h/2(2 × π × r)
= (2 × r × r × π)/2
Rearranging this us get
Area = πr2
Now the area the a semicircle is equal to fifty percent of the of a full circle.
Therefore,
Area that a semicircle =(πr2)/2
Semi circle Formula
The listed below table mirrors the formulas connected with the semicircle the radius r.
Area | (πr2)/2 |
Perimeter (Circumference) | (½)πd + d; once diameter (d) is known |
πr + 2r | |
Angle in a semicircle | 90 degrees, i.e. Best angle |
Central angle | 180 degrees |
Semi circle Examples
Example 1:
Find the area that a semicircle that radius 28 cm.
Solution:
Given,
Radius of semi one = r = 28 cm
Area that semi circle = (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 that a semicircle v diameter 7 cm?
Solution:
Given,
Diameter of semicircle = d = 7 cm
Formula because that the one (perimeter) of a semicircle utilizing its diameter = (½)πd + d
Substitute the value of d, us get;
= (½) × (22/7) × 7 + 7
= 11 + 7
= 18
Therefore, the perimeter the the semicircle is 18 cm.
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Frequently Asked concerns on Semicircle
Is a semicircle half the circle?
Yes, a semicircle is fifty percent the circle. The means, a circle have the right to be split into 2 semicircles.