Semi Circle

Semi Circle

A circle is a locus of points equidistant from a given point which is the center of the circle. The common distance from the center of a circle to its point is called radius.

Thus, the circle is entirely defined by its center (o) and radius R.

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Circle

Any lining passing through the center and touched the two end on the circle, for e.g., the AC line on the circle 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 as the semicircle.

Semi Circle

Let us consider a point anywhere in the second half of the circle. Let it be point B

Let us join point A and point C to this point. It is one of the unique property of a semicircle that the triangle formed such that it always have a right angle triangle with AC as the base and AB and BC as respective chords.Semi Circle

Talking about the area of a semicircle

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.

Semi CircleLet us generate the following image. This polygon can be broken into n isosceles triangle(equal sides being radius)Semi Circle

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*3.14*r . So substituting 2*3.14*r for n*s.

Polygon area=h/2(2*3.14*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*3.14*r)

(2*r*r*3.14)/2

Rearranging this we get

Area=πr^2

Now the area of a semicircle is equal to half of that of a full circle

Therefore, the area of a semicircle is equal to

area=(πr^2)/2


Practise This Question

The two intersecting axes or fixed perpendicular lines divide the Cartesian plane into a fixed number of parts.

What are the parts called? Also, what's that 'fixed number'?