Area and Perimeter of Circle and Semi-Circle

Formulas of Area and Perimeter of a Circle and Semi-Circle

AREA:

The Area of a Circle can be found either by its radius or diameter.

Radius of a circle is half of its diameter. That is,

radius = `frac{diameter}{2}`

Or we can say, diameter of a circle is double of its radius. That is,

diameter = 2 (radius)

In terms of radius, formula of Area of a Circle = π r²

where r is the radius of a circle.

Semi-circle is half of a circle.

So, half of area of a circle is an area of semi-circle.

Thus,

In terms of radius, Area of Semi-Circle = `frac{pi r^2}{2}`

In terms of diameter, formula of Area of a Circle =`frac{pi d^2}{4}`

where d is the diameter of a circle.

In terms of diameter, Area of Semi-Circle = `frac{pi d^2}{8}`

PERIMETER:

Perimeter of a Circle is also named as Circumference of a Circle.

The Perimeter of a Circle can also be found either by its radius or diameter.

In terms of radius, formula of Perimeter of a Circle = 2πr

where r is the radius of a circle.

Perimeter of a Semi-Circle consists of two parts: Half circle and a straight line.

Length of half circle = `frac{2pi r}{2}` = πr

Length of straight line = 2r

So,

In terms of radius, Perimeter of a Semi-Circle

= πr + 2r

= r (π + 2)

In terms of diameter, formula of Perimeter of a Circle = πd

where d is the diameter of a circle.

In semi-circle,

Length of half circle = `frac{pi d}{2}`

Length of straight line = d

So,

In terms of diameter, Perimeter of a Semi-Circle

= `frac{pi d}{2}` + d

= d (`frac{pi}{2}` + 1)