Question

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
https://nafccsd3647-fchs-ccl.gradpoint.com/Resource/1998126,72F,0,0,0,0,0/Assets/testitemimages/geometry_b/area/mc129-1.jpg

about 70%
about 80%
about 90%
about 60%


I think it's 70% ... Is that correct?

Answer 1

To figure this out, we need to find the area of the square, and the area of the shaded region. We could then divide the area of the shaded region by the area of the whole square, which will tell us the percent of the square that is shaded.

Lets pick a nice easy value for the length of the side (it doesn't matter how long the side is, so we can use easy numbers.) Lets say the length of a side of the square is 1 foot. Since the area of a square is the side squared, the area of the whole square is 1 square foot.

Now, we can figure out the area of the shaded region. The shaded region is one whole circle, just split up, and its radius is half the length of a side. So its radius is 1/2. The area of a circle, recall, is equal to pi times the radius squared. The radius squared would be 1/4, so the area of the shaded region is pi/4, or about .785 square feet. Now we can figure out the answer.

\[Probability = \frac{ area of shaded region }{ area of whole \square } = \frac{ .785 }{ 1 } = About 80%\]

Answer 2

.. You sir, make it seem very easy. I appreciate it, you don't know how much this helped me. I didn't really understand this lesson.. At all.. Now I do, and I greatly appreciate it. Thank you!

Answer 3

No problem, I'm glad I could help.