A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,
also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs

(a)6root(3) (a)12root(3) (a)9root(3) (a)18root(3)

• AS THE AREA OF SQUARE IS 36... THEN ONE SIDE WILL BE 6...AND THE PERIMETER OF SQUARE WOULD BE 24=PERIMETER OF PQRS......(1)
  
  AND BY GIVEN CONDITIONS WE KNOW THAT PQRS IS A CASE OF ISOCLESS TRAPEZIUM..AS PQ IS PARALLEL TO RSAND PS=QR..
  
  NOW BY (1)....
  PQ+RS+QR+PS=24
  3RS+QR+RS+QR=24
  2RS+QR=12
  NOW BY HIT AND TRIAL
  PQ=9
  QR=PS=6
  SR=3
  NOW WE CAN FIND THE HEIGHT OF TRAPEZIUM PQRS
  WHICH WILL BE 3ROOT3....
  AREA OF TRAPEZIUM= 1/2 *SUM OF PARALLEL SIDES *HEIGHT....
  =1/2*(9+3)*3ROOT3
  = 18ROOT3.
• 8 years agoHelpfull: Yes(12) No(0)
• Ans 18root(3)
  
  Sol- Lets take, QR=PS= a m and RS=b m, So, PQ=3b m
  now if are of a square is 36 sqm, then perimeter is 24
  
  now perimeter of the inscribed quadrilateral is 4b+2a= 24
  so, 2b+a=12
  from this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)
  
  Now, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}
  Here s= 12
  now by trial and error method we can get the solution
  
  appprox area is 18root(3)
  
• 8 years agoHelpfull: Yes(8) No(0)
• sorry in above solution it should be 4x+2y=24
  
  as area of square is 36 so side of square is 6
  so perimeter of squre =4*6=24
  now
  perimeter of quadriltrl=4x+2y=24 (acordng 2 ques)
  and as we know sum of opposite sides of qudrilatal are equal
  s0 4x=2y..
  now solving both equation we get sides ofqudriltrl 9,6,3,6
  now by appling formula of qudriltrl i.e sqrt(s-a)(s-b)(s-c)(s-d) we get the result as 18 root3
  ans =18root3
  Read more at http://www.m4maths.com/frequently-asked-placement-questions.php?ISSOLVED=&page=1&LPP=10&SOURCE=Elitmus&MYPUZZLE=&UID=&TOPIC=&SUB_TOPIC=#yZQfGyfezVyx1qzv.99
• 8 years agoHelpfull: Yes(6) No(0)
• as area of square is 36 so side of square is 6
  so perimeter of squre =4*6=24
  now
  perimeter of quadriltrl=4x=2y=24 (acordng 2 ques)
  and as we know sum of opposite sides of qudrilatal are equal
  s0 4x=2y..
  now solving both equation we get sides ofqudriltrl 9,6,3,6
  now by appling formula of qudriltrl i.e sqrt(s-a)(s-b)(s-c)(s-d) we get the result as 18 root3
  ans =18root3
• 8 years agoHelpfull: Yes(0) No(0)
• I didn't understand the following line submitted by you Abhinav Anand :
  perimeter of quadriltrl=4x=2y=24 (acordng 2 ques)
  Please Explain.
• 8 years agoHelpfull: Yes(0) No(0)
• @Abhinav Anand-
  
  but that property holds true when a quadrilateral is inscribed in a circle, but here its vice versa!!
• 8 years agoHelpfull: Yes(0) No(0)
• option (d)18 root(3)
• 8 years agoHelpfull: Yes(0) No(0)
• 18root(3)
  use herons formula where s= 12
• 3 years agoHelpfull: Yes(0) No(0)