Area of triangle S1 is 36 cm2. Another triangle S2 is made by joining mid-points of S1. Another triangle S3 is made by joining mid-points of S2. This process is repeated indefinitely. What will be the sum of area of all such triangles formed.
Explanation:
We know area of smaller triangle formed by joining mid-points of a triangle is one-fourth of bigger triangle.
∴ Area of S2 = ¼ (Area of S1) = 36/4 Area of S3 = ¼ (Area of S2) = 36/42 Area of S4 = ¼ (Area of S3) = 36/43 ... and so on
∴ Sum of all the areas = 36 + 364 + 3642 + 3643 + ...
This is sum of an infinite GP whose first term is 36 and common ratio = 1/4
∴ Sum of all the areas = 361-14 = 36×43 = 48
Hence, option (a).
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