A square is drawn by joining the mid points of the sides of a square of side 4cm. A third square is drawn inside the second square in the same way and this process continued indefinitely. Determine the sum of areas of all the squares
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Answered by
65
Side of the first square is 4 cm.
side of second square = 2 √2 cm.
Side of third square = 2 cm.
and so on. i.e. 4, 2 √, 2, √2, 1 ......
Thus, area of these square will be,
= 16, 8, 4, 2, 1, 1/2 ....... Hence, Sum of the area of first, second, third square ......
= 16+8+4+2+1+ .....
= [16/{1-(1/2)}] = 32 Cm2.
side of second square = 2 √2 cm.
Side of third square = 2 cm.
and so on. i.e. 4, 2 √, 2, √2, 1 ......
Thus, area of these square will be,
= 16, 8, 4, 2, 1, 1/2 ....... Hence, Sum of the area of first, second, third square ......
= 16+8+4+2+1+ .....
= [16/{1-(1/2)}] = 32 Cm2.
Answered by
32
32cm2 is the answer.
Hope this will help you.
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