Discussion

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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