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(CBSE 2014) 14. (a) In the figure (i) given below, ABC is a right angled triangle, 2B = 90°, AB = 28 cmand BC = 21 cm. With AC as diameter a semicircle is drawn and with BC as radiusa quarter circle is drawn. Find the area of the shaded region.(b) In the figure (ii) given below, ABC is a right triangle right angled at A. Semicirclesare described on AB, BC and AC as diameters. Find the area of the shaded region.(CBSE 2013)A28 cm4 cm3 cm21 cmCC сB.(ii) |
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Answer» ANSWER Given ∠B=90 ∘ ,AB=28cm,BC=21cm Area of shaded region=ar△ABC+area of SEMICIRCLE AC-ar quarter circle BC = 1
×BC×AB+ 2 1
×π( 2 AC
) 2 − 4 1
×π(BC) 2
=[ 2 1
×21×28]+[ 2 1
× 7 22
× 4 1
( 28 2 +21 2
) 2 ]− 4 1
× 7 22
×21×21 =294+[ 28 11
×1225]−346.5 =294+481.25−346.5=428.75㎠ |
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