Infinite Geometric Progression

Geometry Level 2

A square \(B_1B_2B_3B_4\) is formed by joining the midpoints of the sides of a square \(A_1A_2A_3A_4\). A third square \(C_1C_2C_3C_4\) is made in the same way and the process is continued indefinitely.

If \(A_1A_2 = 10 \text{ cm}\), find the sum of the areas of all the squares so formed in \(\text{cm}^{2}\).

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