Xavier Aptitude Test 2016 Paper

Question : 56 of 103

Marks: +1, -0

ΔABC and ΔXYZ are equilateral triangles of 54 cm sides. All smaller triangles like ΔANM, ΔOCP, ΔQPX etc. are also equilateral triangles. Find the area of shape MNOPQRM.

243 $√3$ sq.cm.
486 $√3$ sq.cm.
729 $√3$ sq.cm.
4374 $√3$ sq.cm.
None of these

Validate

Solution:

(b) ∵ AB = 54 cm
and ΔANM, ΔOCP, ΔOPX
are also equilateral triangles
MN = MR = NO = OP = PQ = QR =

54/3

= 18 cm
and MNOPQRM is a hexagon.
So Area of hexagon =

\ {3 \√{3}}/{2} \√(18)^{2}=486 \√{3} \ {cm}^{2}

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