ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point is selected at random in the square. Calculate the probability that it will liein the triangle MCN.
+128407 See the diagram :
Let the side of the square = S
Then the area of the square = S^2
Note that MC, NC = (1/2)S
And triangle MCN is a right triangle with MN, NC the legs
The area of this triangle = (1/2) (Product of the leg lengths) = (1/2) [ (1/2S * (1/2) S [ = (1/8) S^2
So....the probability that the point lies within triangle MCN =
Area of triangle MCN
_________________ =
Area of square
(1/8) S^2
________ =
S^2
1
_______
8
