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Maths / Mensuration / Area of Segment of Circle

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Area of Segment of Circle

Area of segment of circle

The portion (or part) of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

Now let us take the case of the area of the segment AyB of a circle with centre O and radius r

Area of the segment AyB = Area of the sector OAyB - Area of $Delta$ OAB

= $frac{theta }{360}times pi r^{2}-;;area ;;of ;;Delta OAB$

ILLUSTRATION: O is the centre of the circle, and OA = 28 cm. Find the area of minor segment AQB. $[Take sqrt{2}=1.4.]$

Solution:

$large Area; of; sector; OAQBO=pi times r^{2}times frac{theta }{360}$

$=frac{22}{7}times 28times 28times frac{45}{360}$

$=308;cm^{2}$

$large Area ;of;Delta OAB=frac{1}{2}r^{2};;sin;theta$

$large =frac{1}{2}times 28times 28times sin;45^0$

$large =frac{1}{2}times 28times 28times frac{1}{sqrt{2}}$

$large =196 ;;sqrt{2};;cm^{2}$

Area of segment AQBA = area of sector OAQBO - area of $Delta OAB$

$=(308-196sqrt{2})cm^{2}$

$=(308-274.4)cm^{2}$

$=33.6 ;;cm^{2}$

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Area of Segment of Circle

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Taxes