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.
Choose one:  A) 43A  B) 45A  C) 47A  D) 49A  E) 41A
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+A4+A16+...A+A4+A16+...   ⇒A(1+14+116+...)⇒A(1+14+116+...)   The series in the bracket is G.P. and S∞=a1−rS∞=a1−r   ⇒43A⎛⎝11−14⎞⎠⇒43A(11−14) ⇒4343A   43Answer:43A
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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.