# Circles: Area and Perimeter

## Circles: Area and Perimeter Synopsis

**Synopsis**

- The distance around the boundary of the circle is called
**the perimeter or the circumference**of the circle. - Circumference (perimeter) of a circle = πd or 2πr, where d is he diameter, r is the radius of the circle and .

- Perimeter of a semi circle or protractor = πr + 2r
- Perimeter of a quadrant =

- Distance moved by a wheel in 1 revolution = Circumference of the wheel.

Number of revolutions in one minute =

- The region enclosed inside a circle is called its
**area**.

- Area of a circle = πr
^{2}

- Area of a semi-circle =

- Area of a quadrant =
- Circles having the same centre but different radii are called
**concentric circles**.

Area enclosed by two concentric circles = πR^{2}- πr^{2}= π(R^{2}- r^{2}) = π(R + r)(R - r)

Where, R and r are radii of two concentric circles - The part of the circumference between the two end points of the chord is called an
**arc**. In the figure, arc is shown. - A diameter of circle divides a circle into two equal arcs, each known as a
**semi-circle**. - An arc of a circle whose length is less than that of a semicircle of the same circle is called a
**minor arc**. - An arc of a circle whose length is greater than that of a semicircle of the same circle is called a
**major arc**. - Length of an arc =
- The region bounded by an arc of a circle and two radii at its end points is called a
**sector**.

If the central angle of a sector is more than , then the sector is called a**major sector**and if the central angle is less than , then the sector is called a**minor sector**. - Perimeter of sector of angle θ =
- Area of a sector of angle θ =
- Area of major sector = πr
^{2}– Area of minor sector

- A chord divides the interior of a circle into two parts, each called a segment.

The segment which is smaller than the portion of semi-circle is called the**minor segment**and the segment which is larger than the portion of semi-circle is called the**major segment**. In the circle shown, the yellow portion is the minor segment while the non-shaded portion is the major segment. - Perimeter of segment of angle θ =
- Area of minor segment = Area of sector - Area of ΔABC
- Area of minor segment can also be written as:

- Area of major segment = Area of the circle – Area of minor segment

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