SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 61 of 100

Marks: +1, -0

A square and a regular hexagon are drawn such that all the vertices of the square and the hexagon are on a circle of radius r cm. The ratio of area of the square and the hexagon is

$3 : 4$
$4 : 3 √3$
$√2 : √3$
$1 : √2$

Validate

Solution:

(2)

Diagonal of square = 2r cm.
∴ Area of square

= {1}/{2}×(2 r)^{2}

=2 r^{2}

sq. cm.
Area of ΔOAB

= {√{3}}/{4} r^{2}

sq. cm.
∴ Area of hexagon

= {6 √{3}}/{4} r^{2}

= {3 √{3}}/{2} r^{2}

sq. cm.
∴ Required ratio

=2 r^{2} : {3 √{3}}/{2} r^{2}

=4 : 3√{3}

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