A dart is thrown and hits the square target in the diagram...

The target has a circle inscribed in it, and within that circle, is inscribed another square. If the dart is equally likely to hit any point on the target, what is the probability that the dart will land on the shaded area?

Question

A dart is thrown and hits the square target in the diagram...


The target has a circle inscribed in it, and within that circle, is inscribed another square. If the dart is equally likely to hit any point on the target, what is the probability that the dart will land on the shaded area?

anonymous · Answer

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anonymous · Answer

area of the favorable region divided by the total area

anonymous · Answer

so it is now a matter of figuring out what the areas are
small square seems to have a side of length 2, so its area is $2^2=4$
large square has side length $2\sqrt{2}$ so its area is $(2\sqrt{2})^2=8$

anonymous · Answer

Okay, so all I'm doing is dividing the areas and that will give me the answer?

anonymous · Answer

circle has radius $\sqrt{2}$ so area is $\pi r^2=\pi \sqrt{2}^2=2\pi$

anonymous · Answer

shaded region is $2\pi -4$ area of circle minus area of small square

anonymous · Answer

divide that by 8 for your answer

anonymous · Answer

That was more simple than I thought it would be lol

anonymous · Answer

Thanks!

anonymous · Answer

how did you find 2 √2  as the length for the larger square?