The side of a square is 10 m. A second square is formed by joining, in the proper order, the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square, and so on. Find the sum of the areas of all the squares if the process will continue indefinitely.
Question
The side of a square is 10 m. A second square is formed by joining, in the proper order, the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square, and so on. Find the sum of the areas of all the squares if the process will continue indefinitely.
Solution
Sure, let's solve this step by step.
Step 1: Find the area of the first square. The area of a square is given by the formula side^2. So, the area of the first square is 10^2 = 100 square meters.
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