EF = 12
Explanation:
Step 1 :
The square of side 18 in is divided into 3 parts of equal area by the polygonal chain
So we have
Area of the figure ABCE = Area of the figure AECF = Area of the figure AFCD
Step 2 :
Area of figure ABCE is Area of the triangle AME + Area of the trapezium EMBC
Area of triangle AME = 1/2(ME )(AM) where ME is the base and AM = 9 is the height of the triangle ( AM = 9 since M is the midpoint of AB)
Area of triangle AME = 1/2(ME )9 = 9/2(ME)
Area of the trapezium EMBC = 1/2(ME +BC)(MB) Where ME and BC are the 2 parallel sides and MB is the distance between them
Area of the trapezium EMBC = 1/2(ME+18)9 = 9/2(ME+18)
Therefore
Area of figure ABCE = 9/2(ME) + 9/2(ME+18)
= 9/2(ME +ME+18)
But we know that the area of this figure is 1/3 of the area of the square = 1/3(18*18) = 108
So, 9/2(ME +ME+18) = 108 => 2 ME + 18 = 24 = > ME = 3
Step 3 :
Using the same procedure as above we get, FN = 3
Also we have
ME + EF + FN = 18 ( side of the square)
3 + EF + 3 = 18 => EF = 12