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Question

Find the area of  hexagon PQRSTU (in m2) in which QN is  perpendicular to PS, RL is perpendicular to PS, TM is perpendicular to PS, UO is perpendicular to PS such that PO= 4 m, ON=2 m, NM= 6 m, ML=2 m, LS= 6 m, UO= 6 m, TM= 8 m, QN= 2 m, and RL=4 m.


  1. 144

  2. 147

  3. 156

  4. 142


Solution

The correct option is D

142


Area of the hexagon PQRSTU = Area of ΔPQN + Area of quad QRLN + Area of ΔRSL + Area of ΔTMS + Area of quad OMTU + Area of ΔPOU

=( 12  ×  PN   ×   QN) + {12   × (RL+QN)   ×   NL} + (12   ×   LS  × RL) + (12   ×   MS   × TM) + {12   ×   (TM+UO)   ×   OM} + (12   × PO   ×   UO)

= (12   ×   6   ×   2) + {12  ×  (4+2)   ×   8} + (12   ×   6   ×   4) + (12   × 8   ×   8) + {12   × (8+6)   ×   8} + (12   ×   4   ×   6)

= 6 + 24 + 12 + 32 + 56 + 12

= 142 m2

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