A Nice Geometry Problem (2)

Geometry Level 3

If the pattern continues infinitely and the length side of the larger square is 1. What is the total area of the gray region?

1-\frac{\pi}{2}

2-\frac{\pi}{3}

4-\frac{\pi}{2}

2-\frac{\pi}{2}

2-\frac{\pi}{4}

1 solution

Sanad Kadu
May 24, 2018

Adding the grey area and using Pythagoras Theorem to find sides of squares. We get

$A=1-\pi /4 + 1/2-\pi/8+...........$

From Sum of infiite GP we get ,

$A=(\frac{1-\pi /4}{1-1/2}$ )

$A=2-\pi/2$