Question

Need Help Fast!!! 10 points!

Answer 1

EF = 12

Step-by-step 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