Question

find the area of the shaded region in the given figure if PR=24cm PQ=7cm and O is the centre of the circle ( Use Pie =22/7)

Answer 1

Given that : length of chord ( PR ) = 24 cm.

and,

Length of another chord ( PQ ) = 7 cm.

Diameter of circle ( QR ) = ?

In right angled triangle RPQ ,

PR = 24 cm and PQ = 7 cm.

By Pythagoras theroem,

QR² = PR² + PQ²

QR² = (24)² + (7)²

QR² = 625

QR = √625 = 25 cm.

Diameter ( QR ) = 25 cm.

Radius ( OQ ) = QR/2 = 25/2 = 12.5 cm

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Area of circle = πr²

=> 22/7 × 12.5 × 12.5

=> 491.07 cm².

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Area of triangle= 1/2 × PQ × PR

=> 1/2 × 24 × 7

=> 84 cm².

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Area of semicircle = 1/2 πr²

=> ( 1/2 × 22/7 × 12 . 5 × 12.5 ) cm²

=> 245.53 cm²

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Area of shaded region = Area of circle - ( Area of triangle + Area of semicircle )

=> [ ( 491.07 ) - ( 84 + 245.53 ) ] cm²

=> ( 491.07 - 329.53 ) cm²

=> 161.54 cm²

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