In the diagram below, the areas of the triangles are as follows: A1=1024, A2=1016, A3=1057. What is the area of A4?

















a. 1032

b. 1036

c. 1020

d. 1065

• A1=a.h1/2,A3=a.h2/2,h1=h2=b;
  h2=b-h1;
  1024=a.h1/2.1057=a.(b-h1)/2;
  1057=(ab/2)-(ah1/2);
  ab=4162;
  the total area of the reactangle is A=a.b, A=4162;
  A4=A-(A1+A2+A3)
  A4=1065
• 5 years agoHelpfull: Yes(2) No(5)
• consider area of 1st triangle = A1 = (1/2)*b*h1;
  i,e 1024 = i/2*bh1;
  bh1 = 2048;-----(1)
  Area of 3rd triangle = A3 = (1/2) *b*h2;
  bh2 = 2114;-----(2)
  Now, let Height of 4th triangle be H
  where, H = h1 + h2;
  therefore, h2 = H - h1;
  from (2) we get b(H-h1) = 2114;
  bH - bh1 = 2114
  bH = 2114 - bh1
  bH = 2114 - 2048 from(1)
  Therefore total area => bH = 4162
  now A4 = Total area - (A1+ A2 + A3)
  A4 = 4162 - 3097
  A4 = 1065
• 5 years agoHelpfull: Yes(2) No(1)
• Where is the diagram n where we get this?
• 3 years agoHelpfull: Yes(1) No(0)
• Diagram is not visible
• 3 years agoHelpfull: Yes(0) No(0)
• First we will use triangles with the areas A1 and A3:
  
  A1 = a · h1 / 2 and A3 = a · h2 / 2, where h1 + h2 = b
  
  Then: h2 = b - h1
  
  1024 = a · h1 / 2 1057 = a · ( b - h1 ) / 2
  
  ( we multiply both sides of the equations by 2 )
  
  2048 = a · h1 2114 = a b - a h1
  
  Therefore: 2114 = a b - 2048
  
  a b = 2048 + 2114 = 4162
  
  And the area of the rectangle is A(total) = a b
  
  A4 = A(total) - ( A1 + A2 +A3 ) = 4162 - ( 1024 + 1016 + 1057 ) =
  
  = 4162 - 3097 = 1065
  
  Answer: The area of A4 is 1065.
• 2 Months agoHelpfull: Yes(0) No(0)