trapezium is a quadrilater with at least two sides parallel to each other. four triangles are forme using its diagonals. Area of triangles adjacent to parallel sides is A and B. find area of trapezium in terms of A and B.

• let sides of trap is l1 &l2,and heights of traingle is h1&h2
  area of trap=1/2(l1+l2)(h1+h2)=A+B+1/2*l1*h2+1/2*l2*h1
  also h1/h2=l1/l2 i.e l1*h2=l2*h1
  so area of trap=A+B+l1*h2
  now A=1/2*l1h1 i.e l1h1=2A
  similarly l2h2 =2B
  so l1h1*l2h2=4AB i.e l1h2^2=4AB i.e l1h2=2sqrtAB
  so area of trap = A+B+2sqrtAB
• 7 years agoHelpfull: Yes(14) No(1)
• where are the options??
• 8 years agoHelpfull: Yes(2) No(0)
• I don't remember the options guys, i could not solve it. First option was (√A√B)^2. Other options i don't recall. But they were like 2(A+B) + √AB, 2AB + A+B.
  
  It was also given (not sure) that the other two triangles have same area.
  
  I started solving it by taking a square of side 2 (since square is also a trapezium), taking two opposite triangles as having area A and B. But, I didn't had time so i just moved on.
• 8 years agoHelpfull: Yes(2) No(0)
• C is the answer, so pls go with it ...
  
• 8 years agoHelpfull: Yes(0) No(0)
• u didn't give the options!!
• 8 years agoHelpfull: Yes(0) No(1)
• 2sqrt of A and sqrt of B
• 8 years agoHelpfull: Yes(0) No(0)
• product of areas of two opposite triangles is equall to other two opposite triangles
  AB=CD (1)
  Let K be the area of trepezium
  thus K=A+B+C+D
  or K=A+B+2SQRT(AB)-2SQRT(CD) +C+D -( FRM (1))
  or K=(SQRT A+SQRT B)^2 +(SQRT C-SQRT D)
  NOW in a trepezium
  area of triangles adjacent two parallel sides and formed by diagonal is
  (a^2 h)/2(a+b) and (b^2 h)/(a+b)
  and other two is
  abh/(2(a+b)
  thus C AND D have equall areas thus C-D=0
  
  and K=(SQRT A+SQRT B)^1/2
• 8 years agoHelpfull: Yes(0) No(5)
• ans.-(root A+root B)^2
• 7 years agoHelpfull: Yes(0) No(0)
• sm1 plz explain me in detail
  
• 7 years agoHelpfull: Yes(0) No(0)
• ar trapezium=1/2*(add of parallel lines)*height
  Area of triangles adjacent to parallel sides is A and B
  now, ar trapezium= 1/2*(l1+l2)*h
  =(1/2*l1*h)+(1/2*l2*h)
  =A+B
• 7 years agoHelpfull: Yes(0) No(3)
• any one explain the equation plz
  area of trap=1/2(l1+l2)(h1+h2)=A+B+1/2*l1*h2+1/2*l2*h1
  
  when i m calculating it is coming like this 1/2(l1+l2)(h1+h2)=A+B+1/2*l1*h1+1/2*l2*h2
• 6 years agoHelpfull: Yes(0) No(0)