Perimeter and Area of the Semi-circle

The perimeter of the semi-circle is half of the circumference of the given circle plus the length of diameter as the perimeter is the outer boundary of the figure.

Circumference of semi – circle =\dfrac{2\pi}{2}+d=\pi r+2r

Area of the semi-circle is just half of the area of the circle.

Area of semi – circle =\dfrac{\pi r^2}{2}

Area of a Ring

Area of the ring i.e. the coloured part in the above figure is calculated by subtracting the area of the inner circle from the area of the bigger circle.

Area of the ring =\pi R^2-\pi r^2=\pi(R^2-r^2)

Where, R = radius of outer circle

r = radius of inner circle

Areas of Sectors of a Circle

The area formed by an arc and the two radii joining the endpoints of the arc is called Sector.

Minor Sector

The area including \angle AOB with point C is called Minor Sector. So OACB is the minor sector. \angle AOB is the angle of the minor sector.

Area of the sector of angle \theta=\dfrac{\theta}{360}\times \pi r^2

Major Sector

The area including \angle AOB with point D is called the Major Sector. So OADB is the major sector. The angle of the major sector is 360° – \angle AOB.

Area of Major Sector =\pi r^2-   Area of the Minor Sector

Length of an Arc of a Sector of Angle  \theta

An arc is the piece of the circumference of the circle so an arc can be calculated as the \theta part of the circumference.

Length of an arc of a sector of angle \theta=\dfrac{\theta}{360^o}\times 2\pi r

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