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Maths-

General

Easy

Question

If BC pass through the centre of the Circle, then the Area of the shaded region in the given figure is.....sq units

$\frac{a^{2}}{2} (3 - π)$
$a^{2} (\frac{π}{2} - 1)$
$2 a^{2} (π - 1)$
$\frac{a^{2}}{2} (\frac{π}{2} - 1)$

The correct answer is: $fraction numerator a to the power of 2 end exponent over denominator 2 end fraction open parentheses fraction numerator pi over denominator 2 end fraction minus 1 close parentheses$

Radius of the given circle =BC = $square root of 2 a$ cm (pythagoras theorem)
Area of the shaded region = area of the circle - area of the right angled triangle
$A r e a space o f space t h e space c i r c l e equals πR squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight pi left parenthesis root index blank of 2 straight a right parenthesis squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 straight pi a to the power of 2 to the power of blank end exponent space s q space u n i t$
Area of the triangle =1/28base*height
= $1 half cross times a cross times a 1 half cross times a squared space s q space u n i t$

$A r e a space o f space s h a d e d space r e g i o n space equals 2 πa squared space minus 1 half straight a squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 over 2 πa squared space sq space unit$

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