from an equilateral triangle with area 3 units, new triangle is formed using the midpoints of each side.the process continues indefinitly for the newly formd equltrl triangle.what is the sum of areas of all trinagls

• Area of equilateral triangle=3units
  Now midpoints are joined to form new equilateral traingle area becomes 1/4 th of the orginal one..
  Hence the process continues to infinity
  Therefore,
  3+3*1/4+3*1/16+.... to infinity
  This is the sum of an infinite gp wid common ration=1/4
  Sum of all such areas= 3/(1-1/4)=3*4/3=4 units
• 9 years agoHelpfull: Yes(45) No(1)
• ans = 4 unit
  area of equilateral triangle= 3 unit
  when we form a new triangle using the mid point of each side then the area of new triangle will be =area of original triangle/4
  similarly for 2nd form triangle area=area of original triangle/4^2
  this process continue till infinity
  so sum of area of all formed triangle=3+(3/4)+(3/4^2)+............
  =3(1/(1-1/4))
  =3*4/(4-1)
  =4unit
• 9 years agoHelpfull: Yes(6) No(1)