Area and Perimeter of a 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 = 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)

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