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.

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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)


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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.

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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.

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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 semicircle90 degrees, i.e. Right angle
Central angle180 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.