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 $\text{cm}^{2}$ .