What is the probability that the dart will land in the shaded(black) area?
Oops, not a good drawer. LOL! Imagine this, but the circle is cut in fourths, and two pieces are shaded black. https://www.google.com/search?q=circle+inscribed+in+a+square&safe=active&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiltpGloIXfAhWEdN8KHZjOBbIQ_AUIDigB&biw=1600&bih=789#imgrc=nTA5tZW-9cTF_M:
If the circle is inscribed in the square....let the side of the square = S...so...its area = S^2
The radius of the circle is S/2
So....the area of the circle is pi (S/2)^2 = (pi/4)S^2
And the black area is (1/2) of this = (pi/8)S^2
So....P(hitting the black area) = Black Area / Total Area of Square =
(pi/ 8)S^2 pi / 8 ≈ .3927 = 39.27%