there is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.

• Area of equilateral triangle =(root(3)/4)*a^2=A(given)
  side of triangle=a
  now side is a/2
  then total area A+A/4 +A/16-------
  A/1-(1/4)=A*4/3 is total area
• 9 years agoHelpfull: Yes(19) No(0)
• Ans:- the answer is 4
  Explanation:- Area of Equilateral triangle formed by joining the mid point of an equilateral triangle is 1/4 th of the original triangle .
  So this will form an infinite GP series with common ratio 1/4 and first term =3
  So the Sum will be
  3/(1-1/4)=4
• 9 years agoHelpfull: Yes(5) No(10)
• let the area of the eqilateral tringle=A
  so, the area of the tringle joining the mid point of the sides=1/4A
  and this process is continued.......... means tends to infinity..
  so, this is geometry progression with infinite terms.....
  A+1/4 A+1/16 A+...............infinite terms
  whose first term a=A
  common ratio r= 1/4
  
  Now we can use the formula of the geometry progression s= a/(1-r)
  putting the value in this equation we get ,
  
  A/(1-1/4)
  = 4/3 A is the right ans
• 9 years agoHelpfull: Yes(2) No(0)
• Let ABC is an equilateral triangle with area = A
  Remember: The area of the triangle formed when mid points of the triangle is joined is exactly one-fourth of the bigger triangle. So Area of DEF = A/4. Similarly Area of GHI = A/16 and so on ...
  So Sum of the areas of all triangles = A+A/4+A/16+... ⇒A(1+1/4+1/16+...)
  The series in the bracket is G.P. and S∞=a/1−r
  ⇒A(1/1−1/4⎞⎠⇒ ⇒4A/3
• 9 years agoHelpfull: Yes(1) No(0)