Infinite Geometric Progression

Geometry Level 2

A square B1B2B3B4B_1B_2B_3B_4 is formed by joining the midpoints of the sides of a square A1A2A3A4A_1A_2A_3A_4. A third square C1C2C3C4C_1C_2C_3C_4 is made in the same way and the process is continued indefinitely.

If A1A2=10 cmA_1A_2 = 10 \text{ cm}, find the sum of the areas of all the squares so formed in cm2\text{cm}^{2}.

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