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Sum of areas of all squares
June 20, 2009 - 7:00am
The midpoints of the sides of a 4 centimeter by 4 centimeter square are interconnected to form a smaller square. The midpoints of the sides of the square thus formed are again interconnected to form another smaller square. If the process will be repeated indefinitely, find the sum of the areas of all squares formed including that of the original square.
June 22, 2009 - 7:38pm
#2
Re: Sum of areas of all squares
My answer is 32 cm2. I will show my solution, but not now. 
June 23, 2009 - 8:55pm
#3
Re: Sum of areas of all squares
Uunahan na kita Lj, Hehehe
First Square (the given square)
side, x1 = 4 in
Area, A1 = 42 = 16 in2
Second Square
side, x2 = √(22 + 22) = 2 √2 in
Area, A2 = (2 √2)2 = 8 in2
Third Square
side, x3 = √[ (√2)2 + (√2)2 ] = 2 in
Area, A3 = 22 = 4 in2
Fourth Square
side, x4 = √(12 + 12) = √2 in
Area, A4 = (√2)2 = 2 in2
And the process will continue without end.
Sum of all areas:
A = A1 + A2 + A3 + A4 + ...
A = 16 + 8 + 4 + 2 + ...
The areas are in infinite geometric progression with r = 1/2
S = a1 / (1 - r) = 16 / (1 - 1/2) = 32 in2
See the derivation of formulas of finite and infinite gemetric progressions at Mathalino.com.
August 29, 2009 - 5:57pm
#4
Re: Sum of areas of all squares
yeah boy, wazzap sir!?
November 16, 2009 - 2:47pm
#5
Re: Sum of areas of all squares
ALGEBRA IS NICE SUBJECT
December 23, 2009 - 9:21pm
#6
Re: Sum of areas of all squares
spencerchuy wrote:
ALGEBRA IS NICE SUBJECT
wahhahaha..,,
try mo magsagot ng harvard MIT algebra problems.,,
nakakawindang.,
December 25, 2009 - 9:37am
#7
Re: Sum of areas of all squares
migz wrote:
...try mo magsagot ng harvard MIT algebra problems
Hi migz, share mo sa amin ang link sa MIT algebra problems. Ano pala yung windang? Yay! 
if I'm right!!! the sum of the area of all the square will be 96 square centimeter!!! if I'm wrong please check the addition of all squares that is given!!!
and please give us the correct answer!!!