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.

Guest Feb 14, 2020

#1**+1 **

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

CPhill Feb 14, 2020