The largest of these five squares has side length 27 units, and each additional square's side length is 2/3 as the one before. What is the total area of all five squares? 
The area of the largest square is 27^2 = 729.
The total area is then 729 + 729 (2/3) + 729 (2/3)^2 + 729 (2/3)^3 + 729 (2/3)^4 = 729 + 486 + 324 + 216 + 144 = 1899.
27^2 ==729
[27 *2/3]^2==324
[sqrt(324) * 2/3]^2 ==144
[Sqrt(144) * 2/3]^2 ==64
[Sqrt(64) * 2/3]^2 ==28 + 4/9
729 + 324 + 144 + 64 + 28 + 4/9 ==1,289 + 4/9 - combined area of the 5 squares.
+36915 27^2 + 2/3 * 27 * 2/3 * 27 + .......
= 27^2 + (2/3 * 27)^2 + (2/3)^4 * 27^2 + (2/3)^6 27^2 + (2/3)^8 * 27^2 =
(2/3^0 + 2/3 ^2 + 2/3 ^4 + 2/3 ^6 ) * 27^2 = 1289 4/9 units^2
Double check:
27^2 + 18^2 + 12^2 + 8^2 + (5 1/3)2 = 1289 4/9 <===CHECK !
