Math Problem - Infinite Square

This question is from SIPENMARU (Admissions Selection) in 1987. If today is  SNMPTN.

Problem:
Total area of this square is ....

A. 2a^2
B. 3a^2
C. 4a^2
D. 5a^2
E. Infinite

See the solution below !

Solution:
Look the square below:

Suppose that the area of square is L1 = a^2.
Then we have,
x = the root of (1/2 a^2) -- > Use Phytagoras Theorem

The area of second square = L2 = x^2 = 1/2 a^2.
Then,
L1 + L2 + L3 + ....= a^2 + 1/2 a ^2 + ....

You know that this equation above is Geometry Series, with Rasio (r)

r = 1/2 a ^2  / a^2 = 1/2

Finally we have,

S~ = a / 1 - r = a ^2 / 1- 1/2 = 2a^2.

So the answer is A. 2a^2.