LIC AAO Model Paper 6

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Question : 42 of 160

Marks: +1, -0

In the figure, ABCDEFGH is a regular octagon. What fraction of its area is shaded ?

$1/3$
$1/4$
$1/5$
$3/8$
None of these

Solution:

Area of octagon = 8 ×

√3/4 x^2

=

2√3 x2

where , x = AB
Area of ABCH
=

1/2

(2x + x) × AI
=

1/52

× 3x ×

√{x^2-x^2/4}

=

1/2

× 3x ×

{√3x}/2

=

{3√3}/4 x^2

Required shaded portion =

{3√3}/4 x^2

+

2√3 x^2

=

3/8

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