Geometric Probability

[Nori]

Sorry if this is a duplicate post, but I forgot to share my process on it:
I tried finding the side length of the square by cutting up the square into triangles, i found that the side length is 1.41 in.

and then I did 3.14 - 0.32/3.14 = .8985
so 89.9%? That is what I got but it was incorrect.

Again I apologize if this is a duplicate post.

 

[Deleted member 4993]

View attachment 13675
Sorry if this is a duplicate post, but I forgot to share my process on it:
I tried finding the side length of the square by cutting up the square into triangles, i found that the side length is 1.41 in.

and then I did 3.14 - 0.32/3.14 = .8985
so 89.9%? That is what I got but it was incorrect.

Again I apologize if this is a duplicate post.

What is the strategy here?

The probability of point being inside the green square (area = A_S) as opposed to the space within the circle (area = A_C)

Probability = [A_S] / [A_C)]

A_S = (\(\displaystyle \sqrt{2}\))² = 2

A_C = (\(\displaystyle \frac{\pi}{4}\)) * d² = (\(\displaystyle \frac{\pi}{4}\)) * 2² = \(\displaystyle \pi\)

Continue....