ABCD is a trapezium with AB parallel to CD. AC is perpendicular to BC and BD is perpendicular to AD. If AD=BC=15cm and AB=25cm , find the area of the trapezium ABCD.

1) 192 cm^2
2) 232 cm^2
3) 172 cm^2
4) None of these
5) Cannot be Determined

• The Answer will be 192 cm^2
  
  we can find out the area of triangle ADB
  so height for this triangle wud be equal to the height of trapezium.
  
  so we get height = 12cm.
  now we can easily get to CD=7cm
  
  and we know area of trapezium =1/2*(AB+CD)*HEIGHT
  
  NOW,1/2*(25+7)*12 = 192 cm.
  
  how to get CD=7 cm
  
  when we will drop two perpendicular lines from D to AB as point E and from C to AB as point F.
  
  So,we can see that EF = CD (as the line drawns were perpendicular)
  
  Now In triangleADE,
  We know AD=15 and DE=12
  So we can easily find AE = 9
  
  Similarly from triangleBCF,
  we will get BF = 9cm
  
  therefore,EF = AB -(AE+BF) = 25 - 18 =7cm.
  
  Hope it Helps.:)
• 6 years agoHelpfull: Yes(0) No(2)