 # Semi Circle

## Semicircle Definition

A semicircle is formed when a lining passing through the center touches the two end on the circle.

For e.g., The line AC 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 to as the semicircle. 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 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.

## Area of SemiCircle

The area of a semicircle is half 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 half of the circle. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) or πr, where r is the radius.

Therefore,

 Perimeter of Semicircle = 1/2 π d or πr ### Semi Circle Shape

When a circle is cut in half or when the circumference of a circle is divided by 2, we get Semicircle shape. 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. 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. Let us generate the following image. This polygon can be broken into n isosceles triangle(equal sides being radius) 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=πr2

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=(πr2)/2